Curriculum Vitæ – HW Broer
January 6, 2015
1 Personal
Private data
Hendrik Wolter Broer
Date of birth 18 February 1950
Married to Dr Trijntje Roggen
(parents of four children)
Johann Bernoulli Institute for Mathematics and Computer Science
University of Groningen
PO Box 407
9700 AK Groningen
The Netherlands
Bernoulliborg (room 472)
Nijenborgh 9
9747 AG Groningen
The Netherlands
Phone: +31 50 363 3959
+31 50 363 3975 (secr.)
Fax: +31 50 363 3800
E-mail: h.w.broer@rug.nl
URL: http://www.math.rug.nl/˜broer
Education
Ph.D. 1979 Mathematics and Natural Sciences (University of Groningen)
M.Sc. 1974 Mathematics (University of Groningen)
B.Sc. 1971 Mathematics, Physics and Astronomy
(University of Groningen)
Secondary School (HBS-B) 1967, Meppel, The Netherlands
Academic position
Professor of Dynamical Systems, University of Groningen
Member Royal Netherlands Academy of Arts and Sciences (KNAW)
Afdeling Natuurkunde, chairman Sectie Wiskunde
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Membership professional Societies
Koninklijk Wiskundig Genootschap (KWG)
American Mathematical Society (AMS)
Society for Industrial and Applied Mathematics (SIAM)
Mathematical Association of America (MAA)
2 Professional service and management
Groningen University
Chairman Johann Bernoulli Foundation for Mathematics
(organizes annual JB Lectures for a general audience)
Professional service elsewhere
Chairman Sectie Wiskunde (mathematics section) KNAW
Member PWN Research Committee
Member Program Committee Nationale Wiskundedagen (NWD)
(annual grand scale national meeting secondary school teachers)
Editorial boards
Editor in Chief Indagationes Mathematicæ (under the auspices of KNAW)
Editor Discrete and Continuous Dynamical Systems – Series S
Editor MIHMI (J. Indonesian Mathematical Society)
Past services
Scientific director Johann Bernoulli Institute (JBI)
for Mathematics and Computer Science 2009-2014
Head of Group Dynamical Systems & Mathematical Physics 1996-2014
Director School of Mathematics and Computing Science
(opleidingsdirecteur Wiskunde & Informatica) 1997-2002
Chairman (and vice chairman) Koninklijk Wiskundig Genootschap (KWG)
2006-12
(co-initiator of the Platform Wiskunde Nederland (PWN))
Managing director NWO-cluster Nonlinear Dynamics of Natural Systems
(NDNS+) 2005-11
Chairman Chamber of Mathematics VSNU 2001-06
(one major achievement was foundation of the nationwide
master education in mathematics, named Mastermath)
Member Mathematics Board Lorentz Center Leiden University 2005-09
Scientific Secretary FOM Programme Mathematical Physics 2003-2007
2
Chairman Board National Mathematics Research Institute (MRI) (2005-10)
Division editor Journal of Mathematical Analysis and Applications
(division Ordinary Differential Equations & Dynamical Systems)
2005-09
Member OCW-committee (stuurgroep) Natuur, Leven & Technologie (NLT)
Member OCW-committee Mathematics (Vernieuwingscommissie Wiskunde)
Commissie Toekomst Wiskundeonderwijs (cTWO) (2005-13)
Editor Epsilon-Uitgaven, Utrecht / Amsterdam 1990-2012
Meetings organized
- Workshop Dynamical Systems & Bifurcations (with B.L.J. Braaksma
and F. Takens) Groningen 1984
- Workshop Geometry and Analysis in Nonlinear Dynamics (with F.
Takens) Groningen 1989
- Bernoulli Workshop Dynamical Systems (with I. Hoveijn, S.A. van
Gils and F. Takens) Groningen 1995
- Workshop Finite Dimensional Dynamical Systems (with G. Vegter)
Lorentz Center Leiden 1997
- Workshop Global Analysis of Dynamical Systems (with B. Krauskopf
and G. Vegter) Lorentz Center Leiden 2001
- Large scale conference Equadiff 2003 (with F. Dumortier, J. Mawhin,
A. Vanderbauwhede and S.M. Verduyn Lunel) Hasselt 2003
- Workshop Nonlinear Dynamics, Ergodic Theory and Renormalization
(with A.C.D. van Enter, M. Martens and F. Takens) Lorentz Center
Leiden 2004
- Large scale conference European Nonlinear Oscillator Conference
2005 (with D.H. van Campen, H. Nijmeijer and F. Verhulst) Eindhoven 2005
- Workshop Mathematics of Life Sciences (with A. Doelman, S.M. Verduyn Lunel and A. van der Vaart) Groningen 2005 (in NWO-cluster
NDNS+)
- Workshop Dynamics of Nonlinear Waves (with A. Doelman, M. Haragus and Th. Gallay) Groningen 2006 (in NWO-cluster NDNS+ )
- Workshop Mathematics of Earth Sciences (with H.A. Dijkstra, A. Doelman and H.E. de Swart) Groningen 2006 (in NWO-cluster NDNS+)
- Slotsymposium FOM/NWO programma Mathematische Fysica (with
R.H. Dijkgraaf, N.P. Landsman and A.C.D. van Enter), Amsterdam
2007
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- Workshop The chaotic and ergodic Properties of ‘real’ Hamiltonian
systems (with Paul Tupper) workshop Centre de Recherce Math´ematiques
de Montr´eal CRM/ISM 2007
- Workshop KAM Theory and its applications (with H. Hanßmann and
M.B. Sevryuk), Lorentz Center 2008 (in NWO-cluster NDNS+)
- Workshop New Directions in Dynamical Systems (with S.J. van Strien,
H. Hanßmann, A.J. Homburg, G.B. Huitema and F. Takens), Lorentz
Center 2009
- Workshop Nonlinear Dynamics of Natural Systems (with A. Doelman,
A. van der Vaart, S.M. Verduyn Lunel; local organizers A. Muntean,
M.A. Peletier), EURANDOM TU/e 2010 (in NWO-cluster NDNS+)
- Special Session Complexity of Geometry and Analysis of Larger Scale
Dynamical Systems (with Carles Sim´o, Renato Vitolo and Gert Vegter): The 8th AIMS Conference on Dynamical Systems, Differential
Equations and Applications, Dresden University of Technology 2010
- Workshop Coherent Structures in Dynamical Systems (with Francisco
J. Beron-Vera, Mara J. Olascoaga and Thomas Peacock), Lorentz Center, May 2011
- Workshop Extreme Events in chaotic systems with applications to the
weather (with Mark Holland, Alef Sterk and Pau Rabassa), Groningen
University, May 2012
- Workshop Resonance and Synchronization (with Domien Beersma and
Henk Nijmeijer), Lorentz Center, August 2012
3 Teaching
Professionalisation and didactic schooling attended
A first degree teaching licence Mathematics was already obtained during
the 1970’s
Contribution to various ‘Facultaire Onderwijsdagen’ (initially co-organized
by me, as the director of the school of Mathematics and Computer Science)
Workshops:
Het schrijven van een scriptie Talencentrum RUG, June 2003
Introductie Curriculum Ontwerp Hanzehogeschool, June 2004
Quo Vadis Hanzehogeschool, October 2004
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Opleidingsprofiel Hanzehogeschool, November 2004
Flexible Science Bachelor Hanzehogeschool, February 2006
Masterclass Mentoring Geertruida Gasthuis, November 2010
Undergraduate courses 1997-2009
Kaleidoscoop van de Wiskunde - Ori¨entatie Wiskunde: all years till 04
Calculus op Oppervlakken - Meetkunde en Natuurkunde: 97-98, 98-99, 9900, 00-01, 01-02
Chaos Theorie (AVV & verdiepende minor): 07-08, 08-09, 09-10, 10-11
Perturbation Theory: 97-98, 99-00,01-02, 03-04
Hamiltonian Mechanics: 98-99, 00-01, 04-05, 06-07
Advanced Differential Equations: 03-04, 04-05, 05-06, 06-07, 07-08, 08-09
Dynamical Systems & Chaos: 09-10, 10-11
Student Colloquium (Algebraic Topology): 07-08, 08-09
Seminar Dynamical Systems: all years
A number of times the master courses Perturbation Theory or Hamiltonian
Mechanics and Seminar Dynamical Systems have been included in the national MRI Masterclass
The course Hamiltonian Mechanics under the name Classical Mechanics &
Dynamical Systems in 2004-05 and 2007-08 (to be continued 2010-11) was
included in the National Curriculum Master Courses Mathematics Mastermath (coordinated by the VNSU). See below under ‘Other educational activities’.
During the 1990-91 period courses occur like Krommen en Oppervlakken I,
Dynamische Systemen, Metrische Ruimten, Analyse op Vari¨eteiten en Voortgezette Differentiaalvergelijkingen & Dynamische Systemen.
Undergraduate student projects: students + subjects
1. Fabian Vermeer, Een dubbele Hopf-bifurcatie 1988
2. Henk P Bruin, Computation and visualisation of invariant manifolds
1990
3. Jan Scholtmeijer, Hamiltoniaanse mechanica en stabiliteit van het Zonnestelsel 1992
4. Janita Wilting, Errors in discrete scale-space derivatives; influences of
order, scale and discretization 1994 (jointly with MA Viergever, AZU
(UMCU))
5. Martijn van Noort, De berekening van invariante vari¨eteiten in R3
1996
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6. Whee Ky Ma, Aspects of Noncommutative Geometry 1997
7. Heleen van der Meer, Influences of changing seasons on a predatorprey model 1997
8. Krista Homan, Routes to chaos in the Lorenz-84 atmospheric model
1997
9. Rutger Kock, Routes to chaos in the periodically driven Lorenz-84
system 1998
10. Bart Oldeman, Analysis of resonances in the Three-Body-Problem using planar reduction 1998
11. Gerton Lunter, Hamiltonian normal forms, an algorithmic approach
1999
12. Hendrikjan Schaap, Separatrix-passage en gevangen zijn in resonantie
2000
13. Renate van der Kooij, Time discounting in resource dilemma situations
2000 (jointly with IVEM)
14. Hanneke Molenaar, Bifurcations from regular to chaotic behaviour in
the Lorenz-84 climate model 2001
15. Samuel Severijnse, Impliceert onvoorspelbaarheid willekeur? 2001
16. Jun Hoo, Matrices depending on parameters, with focus on some resonant Hamiltonian cases 2001
17. Hengki Tasman, The Hopf Hopf bifurcation 2001
18. Khairul Saleh, The Hopf Saddle-Node bifurcation 2001
19. Ronald van Dijk, Strong normal-internal resonances in quasi-periodically
forced oscillators 2007
20. Monique van Beek (bachelor), Crazy things in R, 2008
21. Laura Siekman (together with IDO), Chaos between dimensions 2 and
3, 2009
22. Thomas de Jong (bachelor) Dynamics of chaotic systems and fractals
2009
23. Kim van Oost (together with IDO), Lissajous figures and the like 2011
24. Thomas de Jong, Aspects of KAM Theory 2012
25. Luuk van Disselhorst (bachelor), The Poincar´e–Hopf index 2012
Percentage of teaching
Over the last couple of years 30 - 40 %.
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PhD Supervisor: completed and current projects
1. George B. Huitema, Unfoldings of quasi-periodic tori. University
of Groningen, February 1988. Promotor: B.L.J. Braaksma, referent:
H.W. Broer. (Funded by the Netherlands Organisation for Scientific
Research NWO.)
2. Bernd Krauskopf, On the 1:4 resonance problem. University of Groningen, June 1995. Promotores: F. Takens and H.W. Broer.
3. Heinz Hanßmann, Quasi-periodic motions of a rigid body, a casestudy on perturbations of superintegrable systems, University of Groningen, October 1995. Promotor: H.W. Broer, referent: R.H. Cushman.
4. Hinke M. Osinga, Computing invariant manifolds, variations on the
graph transform. University of Groningen, June 1996. Promotor:
H.W. Broer, co-promotor: G. Vegter. (Funded by the Netherlands Organisation for Scientific Research NWO.)
5. Florian O.O. Wagener, On the skew Hopf–bifurcation. University of
Groningen, January 1998. Promotores: F. Takens and H.W. Broer.
(Funded by the Netherlands Organisation for Scientific Research NWO.)
6. Gerton A. Lunter, Bifurcations in Hamiltonian systems: Computing
singularities by Gr¨obner bases. University of Groningen, December
1999. Promotor: H.W. Broer, co–promotor: G. Vegter.
7. Hans H. de Jong, Quasiperiodic breathers in systems of weakly coupled pendulums: Applications of KAM theory to classical and statistical mechanics. University of Groningen, December 1999. First promotor: H.W. Broer, second promotor: M. Winnink, referent: A.C.D. van
Enter. (Funded by the Netherlands Organisation for Scientific Research NWO (FOM).)
8. Evgeny Verbitskiy, Generalized entropies in dynamical systems. University of Groningen, October 2000. Promotores: F. Takens and H.W. Broer.
(Funded by the Netherlands Organization for Scientic Research NWO.)
9. Martijn van Noort, Global coherent dynamics of the parametrically
forced pendulum: a case study in one–and–a–half degrees of freedom. University of Groningen, May 2001. Promotor: H.W. Broer,
co–promotor: G. Vegter. (Funded by the Netherlands Organisation for
Scientific Research (NWO): Foundations FOM and SMC.)
10. Renato Vitolo, Bifurcations of attractors in 3D diffeomorphisms: a
study in experimental mathematics. University of Groningen, October
2003. Promotor: H.W. Broer, co–promotores: C. Sim´o (University of
Barcelona) and F. Takens.
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11. Maria Cristina Ciocci, Bifurcation of periodic solutions and persistence of quasi–periodic solutions in reversible systems. University of
Ghent, November 2003. Promotor: A. Vanderbauwhede (University
of Gent), co-promotor: H.W. Broer.
12. Taede A. Smedes, Avoiding Balaam’s mistake: exploring Divine action in an age of scientism. University of Groningen, March 2004.
Promotor: L.J. van den Brom, second promotor: H.W. Broer, co–
promotor: A.F. Sanders.
13. Jun Hoo, Quasi–periodic bifurcations in a strong resonance: combination tones in gyroscopic stabilisation. University of Groningen,
January 2005. Promotor: H.W. Broer. (Funded by the Netherlands
Organisation for Scientific Research NWO (FOM).)
14. Khairul Saleh, Organising centres in semi-global analysis of dynamical systems. University of Groningen, December 2005. Promotor:
H.W. Broer, with J.M. Tuwankotta and E. Soewono (ITB-Bandung,
Indonesia) as counterparts. (Funded by the Royal Dutch Academy of
Sciences KNAW and the Dutch Ministery of Economic Affairs.)
15. Iris Gulikers, Reinvention of geometry. University of Groningen, December 2005. Promotor: H.W. Broer, with J.A. van Maanen and
A. van Streun as co–advisors. (Partly funded by the Netherlands Organisation for Scientific Research NWO).
16. Harry Sitters, Sybrandt Hansz Cardinael 1578-1647, Rekenmeester en
wiskundige, zijn leven en zijn werk. University of Groningen, November 2007. Promotores: H.W. Broer and J.A. van Maanen. (Funded by
the Netherlands Organisation for Scientific Research NWO (Program
LION).)
17. Easwar Naga Subramanian, Attractor switching in neuron networks
and Spatiotemporal filters for motion processing. Promotores: H.W.
Broer and N. Petkov, University of Groningen, February 29th, 2008.
18. Olga Lukina, Geometry of torus bundles in Hamiltonian dynamics.
Promotor: H.W. Broer, University of Groningen, September 2008.
19. Sarma Chandramouli, Renormalization and non-rigidity. Promotores:
H.W. Broer, University of Groningen and M. Martens (Stony Brook),
December 2008.
20. Peter Hazard, H´enon-like maps and renormalization. Promotores:
H.W. Broer, University of Groningen and M. Martens (Stony Brook),
December 2008.
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21. Alex Opoku, On Gibbs properties of transforms of lattice and meanfield systems. Promotores: Ch. K¨ulske, A.C.D. van Enter and H.W.
Broer, University of Groningen, 4 September 2009.
22. Sijbo-Jan Holtman, Dynamics and geometry of resonant bifurcations.
Promotores: H.W. Broer and G. Vegter, University of Groningen, 18
September 2009. (Funded by the Netherlands Organisation for the
Advancement of Scientific Research NWO.)
23. Alef Sterk, Atmospheric variability and the Atlantic Multidecadal Oscillation. Part B: Mathematical analysis of reduced models. Promotores: H.W. Broer, H.A. Dijkstra (IMAU) and C. Sim´o (University of
Barcelona), University of Groningen, 1 October 2010. (Funded by the
Netherlands Organisation for Scientific Research NWO, area Earthand Life Sciences.)
24. Jos Tolboom, The potential of a classroom network to support teacher
feedback, a study in statistics education. Promotores: H.W. Broer and
W.A.J.M. Kuiper (SLO), University of Groningen, 15 June 2012.
25. Xia Liu, The discontinuous Hopf-transversal system and its geometric
regularization. Promotor: H.W. Broer. (Funded by the Netherlands
Organisation for Scientific Research NWO, area Exact Sciences - Applied Mathematics.) University of Groningen, 22 February 2013.
26. Hildeberto Jardon Kojakhmetov, Geometric Desingularization of Constrained Differential Equations in Terms of Slow-Fast Systems. Promotores: Henk Broer and Gert Vegter. (Funded by a Mexican scholarship.) Expected defence 12 June 2015.
Current and near-future projects
27. Swier Garst, The dynamics of the Fold and Twist Map. Promotores:
H.W. Broer and J.M. Aarts (Technische Universiteit Delft). Expected
defence 2016.
PhD Examiner and reading committee
1. Igor Hoveijn, Aspects of resonance in dynamical systems, promotor
F. Verhulst, Utrecht 1992.
2. Gert H.M. van der Heijden, Nonlinear drillstring dynamics, promotor
F. Verhulst, Utrecht 1994.
3. Jeroen S.W. Lamb, Reversing symmetries in dynamical systems, promotor H.W. Capel, University of Amsterdam 1994.
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4. Joost Hermans, Rolling rigid bodies with and without symmetries, promotor J.J. Duistermaat, Utrecht 1995.
5. Roland J.P. Boon, Bifurcaton in fluid flow near a boundary surface,
promotores P.G. Bakker and J.W. Reyn, Delft 1997.
6. Willem Cazemier, Proper orthogonal decomposition and low dimensional models for turbulent flows, promotor A.E.P. Veldman, Groningen 1997.
7. Jordi Villanueva, Normal forms around lower dimensional tori of Hamil` Jorba, Universitat Polit`ecnica de Catalunya
tonian systems, promotor A.
(Barcelona) 1997.
8. Stefano Stramigioli, From differentiable manifolds to interactive robot
control, promotores G. Honderd and G.J. Olsder, Delft 1998.
9. Claudia Valls, The classical Arnold example of diffusion with two equal
parameters, promotor C. Sim´o, Universitat de Barcelona 1999.
10. Sebastian Wieczorek, The dynamical complexity of optically injected
semiconductor lasers, promotores D. Lenstra and B. Krauskopf, Vrije
Universiteit Amsterdam 2002.
11. Lennaert van Veen, Time scale interaction in low-order climate models, promotores F. Verhulst and J.D. Opsteegh, Utrecht 2002.
12. Johan M. Tuwankotta, Higher order resonances in dynamical systems,
promotor F. Verhulst, Utrecht 2002.
13. Bob Rink, Geometric dynamics of Hamiltonian lattices, promotores
F. Verhulst and J.J. Duistermaat, Utrecht 2003.
14. Kevin Webster, Bifurcations of reversible systems with application to
the Michelson system, promotor J.S.W. Lamb, Imperial College London 2003.
15. Joaquim Puig, Reducibility of quasi-periodic skew-products and the
spectrum of Schr¨odinger operators, promotor C. Sim´o, Universitat de
Barcelona 2004.
16. Nguyen Huu Khanh, Heteroclinic cycles in thermal convection models, promotores A. Doelman and A.J. Homburg, University of Amsterdam 2005.
17. Olivier Sapin, Flot crois´e aus-dessus d’un sol´eno¨ıde et th´eor`eme de
gap labelling pour l’op´erateur de Schr¨odinger matriciel, promotor
H. Jauslin, Universit´e de Bourgogne (Dijon) 2005.
18. Hendrikjan G. Schaap, Ising models and neural networks, promotores
A.C.D. van Enter and M. Winnink, Groningen 2005.
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19. Nenad Mehajlovic, Torsional and lateral vibrations in rotor/drillstring
systems, promotor H. Nijmeijer, Eindhoven 2005.
20. Hill Meijer, Co-dimension 2 bifurcations of iterated maps, promotores
F. Verhulst and Yu. Kuznetsov, Universiteit Utrecht 2006.
21. Hartmut Erzgr¨aber, Dynamics of delay-coupled semiconductor laser
systems, promotores D. Lenstra and B. Krauskopf, Vrije Universiteit
Amsterdam 2006.
22. Mathilde Kammerer - Colin de Verdi`ere, Bifurcations de vari´et´es invariantes, promotor R. Moussu, Universit´e de Bourgogne (Dijon) 2006.
23. Taoufik Bakri, Averaged behaviour of nonconservative coupled oscillators, promotores F. Verhulst and Yu. Kuznetsov, Universiteit Utrecht
2007.
24. Hicham Zmarrou, Bifurcations of random maps, promotor A. Doelman, co-promotor A.J. Homburg, Universiteit van Amsterdam 2008.
25. Arturo Vieiro, Study of the effect of conservative and weakly dissipative perturbations on symplectic maps and Hamiltonian systems, promotor C. Sim´o, Universitat de Barcelona 2009.
26. Pau Rabassa, Contribution to the study of perturbations of low dimen`
sional maps, promotor Angel
Jorba, Universitat de Barcelona 2010.
27. Erik Steur, Synchronous behavior in networks of coupled systems, with
applications to neuronal dynamics, promotor Henk Nijmeijer, Eindhoven 2011.
28. Jaap Eldering, Persistence of noncompact Normally Hyperbolic Invariant Manifolds in bounded geometry, promotores Erik van den Ban
and Heinz Hanßmann, Utrecht 2012.
29. Quang Sang PHAN, Monodromie spectrale d’op´erateurs non-autoadjoints, promotores Christophe CHEVERRY, Francis NIER, San VU
NGOC, Universit´e de Rennes 1, 2012.
30. Blaz Mramor, Some destructive results in the Aubry–Mather theory,
promotor Rob van der Vorst, VU Amsterdam 2012
Other educational activities
1. Post Academic Courses Chaos and Fractals (December 1990) en Chaos
en Tijdreeksen, March 1993, organized with F. Takens and G. Vegter.
Funded by the participants (via PAON, Leiden).
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2. Participation in Erasmus Intensive Course Mathematical Methods of
Technology: Chaos and Predictability, June 1996 organized by G.
Vegter.
3. MRI (or MRI-Stieltjes) Master Class courses:
- Dynamical Systems and Mathematical Aspects of Classical Mechanics (with S.J. van Strien (UvA) and F. Takens), September
1992-June 1993.
- Dynamical Systems and Perturbation- and KAM-Theory (with I.
Hoveijn and F. Takens) September 1995-June 1996.
- Phenomenology of Dynamical Systems and Algorithmic aspects
of Dynamical systems, (with F. Takens and G. Vegter) September
1997-June 1998.
- Finite and Infinite Dimensional Dynamical Systems (with A. Doelman and S.A. van Gils) September 2005-June 2006.
4. National master course Classical Mechanics & Dynamical Systems or
Hamiltonian Dynamical Systems, under the auspices of the national
Regieorgaan Master-onderwijs Wiskunde, Fall 2004 and Spring 2007
and 2008, 2010 and 2013 (in collaboration with Holger Waalkens and
Heinz Hanßmann.
External Courses:
5. Boston University. Graduate course Perturbation Theory and KolmogorovArnold-Moser Theory, January-May 1985.
6. Limburgs Universitair Centrum. Graduate course Kolmogorov-ArnoldMoser Theory for Families of Dissipative Dynamical Systems, MarchApril 1988
Graduate course Perturbation- and KAM-Theory (Erasmus Project),
February-March 1992.
7. Twente University. One week graduate– / PhD–courses: Introduction to Dynamical Systems and Chaos, Structural Stability, Bifurcation
Theory, KAM-Theory, Classical Mechanics, Homoclinic bifurcations.
Alternating on behalf of the FOM program Mathematical Physics or
the Mathematics Research Institute, 1987, 1988, 1989, 1991, 1997,
2001, 2002.
Graduate– / PhD–course: Singular Perturbation Theory of Differential
Equations, January 2008. Together with A. Doelman, T. Kaper and
M. Krupa.
8. ITB-Bandung Graduate course Dynamical Systems and KAM Theory,
February-March 2001. Together with F.O.O. Wagener.
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Graduate course Catastrophe Theory with Applications to Constrained
Differential Equations and Singular Perturbation Theory, July 2007.
Together with J.M. Tuwankotta and F. Verhulst.
9. Summerschools KAM Theory 2001: At DTU Copenhagen (Lyngby).
At Peyresq (near Nice, under auspices of MASIE).
Miscellaneous:
10. Seniorenacademie Groningen en Drenthe, course Wiskunde door de
Eeuwen Heen, March-April 2007, March-April 2009, March-April
2011 organized with M.C. van Hoorn.
11. Wiskunde D courses Kansrekening en Statistiek en Kepler’s Derde Wet
en de Stabiliteit van het Zonnestelsel for Dutch Highschool teachers
and pupils, Spring 2008.
4 Research
Postdoctoral fellows and guest researchers
1. Dr I. Hoveijn, in NWO-program Mathematical Aspects of Nonlinear Dynamical Systems, 1992–1996.
2. Dr A.L. Hagen, NWO-postdoc, with G. Vegter (PI), 1997–1999.
3. Dr H.P. Bruin, KNAW-fellow, 2000–2003.
4. Dr V. Naudot, FWN-postdoc (compensating for Directorship School of Mathematics and Computer Science), 2001–2005.
5. Dr K. Efstathiou, FWN-postdoc (compensating for Managing Directorship
NWO-cluster NDNS+ and for the scientific directorship JBI), 2005–2012.
6. Dr Pau Rabassa Sans, NWO-postdoc (under the auspices of ComplexityNET European network), 2011–2013.
7. Dr ZHAO Lei, FWN-postdoc (compensating for scientific directorship JBI),
2013–2015.
Moreover I have had quite a number of guests, mostly for 1 or 2 weeks, for
joint research (including joint PhD supervision). Carles Sim´o (Universitat de
Barcelona) and Robert Roussarie (Universit´e de Bourgogne) are often (almost
yearly) in this category. Also Martin Golubitsky (University of Houston), Bernd
Krauskopf (University of Bristol) and Heinz Hanßmann (then RWTH-Aachen,
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presently Utrecht University) have been regular short term guests, often arranged
around a PhD defence. Also many Dutch colleagues have been short term visitors. For the several PhD defences of Jun Hoo, Easwar Subramanian, Olga Lukina, Sarma Chandramoulli, Peter Hazard Sijbo Holtman, Alef Sterk and Xia Liu
short term guests came from abroad, such as Richard Cushman (Calgary), Dmitri
Sadovski´ı (Dunkerque), Sebastian van Strien (Warwick), Carles Sim´o (Barcelona),
Robert MacKay (Warwick) and Robert Roussarie (Dijon). Here quite a few visitors came from within the Netherlands, like Hans Duistermaat (Utrecht), Ale Jan
Homburg (Amsterdam), Ferdinand Verhulst (Utrecht), Florian Wagener (Amsterdam), Arjen Doelman (Leiden), etc.
Mark Levi (Rensselaer Polytechnical Institute / Penn State University) has been
visiting half a year in 1993 and Mikhail Sevryuk (MCCME Moscow) half a year
in 1995, both funded from the NWO Priority Program, mentioned in the next item.
Carles Sim´o (Universitat de Barcelona) has occupied the Johann Bernoulli Chair
2006-2007 for three months totally, funded by the IWI.
Heinz Hanßmann (now Utrecht University) is a 0.2 advisor for 1 year during 20082009, funded by NDNS+, see below. In 2008-2009, 2011-2012 Valery Gaiko from
the Belarus State University (Minsk) paid a one half year visits (NWO bezoekersbeurs).
Grant support
1. All workshops under 2 were funded by the Royal Netherlands Academy
of Arts & Sciences (KNAW) and the Netherlands Organisation for the Advancement of Scientific Research (NWO). Equadiff 2003 moreover was sponsored by the European Science Foundation Prodyn, the Mathematics Research Institute (MRI) and the FOM Program Mathematical Physics.
2. NWO Priority Program Mathematical Aspects of Nonlinear Dynamical Systems with S.A. van Gils (UTwente) and F. Takens, 1993-1997. Amounted
to 1.3 Mf. See 4 for details.
3. NWO Open / Free Competition Mathematics, totally 5 PhD students. The
NWO area Earth- and Life Sciences is funding 1 PhD student. See 3 for
details.
4. FOM program Mathematical Physics, totally 2 PhD students. See 3 for
details.
5. KNAW program Extended Program in Applied Mathematics (EPAM), 1
PhD student, see 3.
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6. From KNAW postdoc program, 1 postdoc jointly with J.M. Tuwankotta (PI)
ITB-Bandung.
7. One postdoctoral three-year KNAW-fellow, see above.
8. NWO cluster Nonlinear Dynamics of Natural Systems (NDNS+) and Ministery of Economic Affairs with A. Doelman (CWI, Amsterdam), S.M. Verduyn Lunel (Leiden) and A. van der Vaart (VU Amsterdam) 2005–2009.
Amounts to 4.0 MEuro, of which 1.7 MEuro for Groningen University
Mathematics research infrastructure.
9. NWO Complexity-NET Predictability of Extreme Weather Events, in cooperation with R. Vitolo (Exeter), M. Holland (Exeter), 21 Months of postdoctoral research.
10. NWO cluster Nonlinear Dynamics of Natural Systems (NDNS+) and Ministery of OCW 2013–2016: three year prefinancing of a tenure track assistant
professor 240 KEuro.
Scientific publications
In international refereed journals
1. HWB, Quasi-periodicitin local bifurcation theory, Nieuw Arch. Wisk. 4(1),
(1983), 1–32.
2. HWB and G. Vegter, Subordinate Sil’nikov bifurcations near some singularities of vector fields having low codimension, Ergod. Th. & Dynam. Sys.,
4, (1984), 509–525.
3. HWB and F.M. Tangerman, From a differentiable to a real analytic perturbation theory, applications to the Kupka Smale theorems, Ergod. Th. &
Dynam. Sys., 6, (1986), 345–362.
4. B.L.J. Braaksma and HWB, On a quasi-periodic Hopf bifurcation, Ann. Institut Henri Poincar´e, Analyse non lin´eaire, 4, no.2, (1987), 115–168.
5. HWB and F. Takens, Formally symmetric normal forms and genericity, Dynamics Reported, 2, (1989), 36–60.
6. HWB, G.B. Huitema and F. Takens, Unfoldings of quasi-periodic tori, Mem.
AMS, 83(421), (1990), 1–82.
7. B.L.J. Braaksma, HWB and G.B. Huitema, Toward a quasi-periodic bifurcation theory, Mem. AMS, 83(421), (1990), 83–175.
15
8. HWB and G.B. Huitema, A proof of the iso-energetic KAM-theorem from
the ‘ordinary’ one, Journ. Diff. Eqns., 90(1), (1991), 52–60.
9. HWB and G. Vegter, Bifurcational aspects of parametric resonance, Dynamics Reported, New Series 1, (1992), 1–51.
10. HWB, S.-N. Chow, Y. Kim and G. Vegter, A normally elliptic Hamiltonian
bifurcation, ZAMP 44, (1993), 389–432.
11. HWB and F. Takens, Mixed spectrum and rotational symmetry, Arch. Rational Mech. An. 124, (1993), 13–42.
12. HWB, Huygens’ isochrone slinger, Euclides, 70(4) (1995), 110–117.
13. HWB and G.B. Huitema, Unfoldings of quasi–periodic tori in reversible
systems, Journ. Dynamics and Differential Equations, 7(1), (1995) 191–
212.
14. HWB and M. Levi, Geometrical aspects of stability theory for Hill’s equations, Archive Rat. Mech. An. 131, (1995), 225–240.
15. HWB, KAM-Theory: Multi–Periodicity in conservative and dissipative systems, Nieuw Arch. Wisk. 14(1), (1996), 1–15.
16. HWB, R. Roussarie and C. Sim´o, Invariant circles in the Bogdanov-Takens
bifurcation for diffeomorphisms, Ergod. Th. & Dynam. Sys. 16, (1996),
1147–1172.
17. HWB, G.B. Huitema and M.B. Sevryuk, Quasi–periodic tori in families
of dynamical systems: order amidst chaos, Springer LNM 1645, (1996),
Springer–Verlag (195 p).
18. HWB, H.M. Osinga and G. Vegter, Algorithms for computing normally hyperbolic invariant manifolds, ZAMP, 48, (1997), 480–524.
19. HWB, De chaotische schommel, Pythagoras 35(5), (1997), 11–15.
20. HWB, I. Hoveijn and M. van Noort, A reversible bifurcation analysis of the
inverted pendulum, Physica D, 112, (1998), 50–63.
21. HWB, G.A. Lunter and G. Vegter, Equivariant singularity theory with distinguished parameters, two case studies of resonant Hamiltonian systems,
Physica D, 112, (1998), 64–80.
16
22. HWB, C. Sim´o and J.C. Tatjer, Towards global models near homoclinic tangencies of dissipative diffeomorphisms, Nonlinearity, 11(3), (1998), 667–
770.
23. HWB, I. Hoveijn, G.A. Lunter and G. Vegter, Resonances in a Spring–
Pendulum: algorithms for equivariant singularity theory, Nonlinearity, 11(5),
(1998), 1–37.
24. HWB and C. Sim´o, Hill’s equation with quasi-periodic forcing: resonance
tongues, instability pockets and global phenomena, Bol. Soc. Bras. Mat.
29, (1998) 253–293.
25. HWB, F. Takens and F.O.O. Wagener, Integrable and non–integrable deformations of the skew Hopf bifurcation, Regular and Chaotic Dynamics 4(2),
(1999), 17–43.
26. HWB, I. Hoveijn, M. van Noort and G. Vegter, The inverted pendulum: a
singularity theory approach, Journ. Diff. Eqns. 157, (1999), 120–149.
27. HWB, The how and what of chaos, Nieuw Arch. Wisk. 5th series 1(1),
(2000), 34–43.
28. HWB and F.O.O. Wagener, Quasi–periodic stability of subfamilies of an
unfolded skew Hopf bifurcation, Archive Rat. Mech. An. 152, (2000), 283–
326.
29. HWB and C. Sim´o, Resonance tongues in Hill’s equations: a geometric
approach, Journ. Diff. Eqns. 166, (2000), 290–327.
30. HWB and C. Sim´o, Reducible linear quasi–periodic systems with positive
Lyapunov exponent and varying rotation number, Journ. Diff. Eqns. 168,
(2000), 60–66.
31. HWB, Quasi-periodicity in dissipative systems, MIHMI (Journ. Indonesian
Math. Soc.), 7(3), (2001), 7–33.
32. HWB, C. Sim´o and R. Vitolo, Bifurcations and strange attractors in the
Lorenz-84 climate model with seasonal forcing. Nonlinearity 15(4), (2002),
1205–1267.
33. HWB, A. Hagen and G. Vegter: Multiple purpose algorithms for invariant
manifolds, Dynamics of Continuous, Discrete and Impulsive Systems, Series
B: Applications and Algorithms, 10(3), (2003), 331-34
17
34. HWB, I. Hoveijn, G.A. Lunter and G. Vegter, Bifurcations in Hamiltonian
systems: Computing singularities by Gr¨obner bases. Springer LNM 1806,
2003.
35. HWB and M. Golubitsky and G. Vegter, The geometry of resonance tongues:
A Singularity Theory approach. Nonlinearity 16 (2003) 1511-1538.
` Jorba, J. Villanueva and F.O.O. Wagener, Normal36. HWB, H. Hanßmann, A.
internal resonances in quasi-periodically forces oscillators: a conservative
approach, Nonlinearity 16 (2003) 1751-1791.
37. HWB, C. Sim´o and J. Puig, Resonance tongues and instability pockets in
the quasi-periodic Hill-Schr¨odinger equation, Commun. Math. Phys., 241,
(2003) 467-503.
38. HWB, Coupled Hopf-bifurcations: Persistent examples of n-quasiperiodicity
given by families of 3-jets, Ast´erisque, 286 (2003), 223-229.
39. HWB, Ken uw klassieken: Kolmogorov in het Concertgebouw. Nederl.
Tijdschr. voor Natuurkunde, jaargang 70 nummer 1 (2004), 20-21.
40. HWB, KAM theory: the legacy of Kolmogorov’s 1954 paper. Bull. AMS
(New Series), 41(4) (2004), 507-521.
41. HWB, I. Hoveijn, M. van Noort, C. Sim´o and G. Vegter, The parametrically
forced pendulum: a case study in 1 12 degree of freedom, Journ. Dynamics
and Differential Equations, 16(4) (2004), 897-947.
42. HWB, Kolmogorov, la ‘K’ de KAM, Butllet´ı de la Societat Catalana de
Matem`atiques, 18(2) (2004), 39-57.
43. HWB, H. Hanßmann and J. You, Bifurcations of normally parabolic tori in
Hamiltonian systems, Nonlinearity 18 (2005) 1735-1769.
44. HWB, V. Naudot, R. Roussarie and K. Saleh, Bifurcations of a predatorprey model with non-monotonic response function, C.R. Acad. Sci. Paris
Ser. I 341 (2005), 601-604.
45. HWB, Wiskunde als kritische succesfactor? Euclides 81(6) (2006), 282285.
46. HWB, H. Hanßmann and J. You, Umbilical torus bifurcations in Hamiltonian systems, Journ. Diff. Eqns. 222 (2006) 233-262.
18
47. HWB, V. Naudot, R. Roussarie and K. Saleh, A predator-prey model with
non-monotonic response function. Regular and Chaotic Dynamics 11(2)
(2006), 155-165.
48. HWB, V. Naudot and R. Roussarie, Catastrophe theory in Dulac unfoldings.
Ergod. Th. & Dynam. Sys. 26 (2006), 1-35.
49. HWB, J. Hoo and V. Naudot, Normal linear stability of quasi-periodic tori,
Journ. Diff. Eqns. 232(2) (2007), 355-418.
50. HWB, H. Hanßmann and J. Hoo, The quasi-periodic Hamiltonian Hopf bifurcations, Nonlinearity 20 (2007), 417-460.
51. HWB, A. Hagen and G. Vegter, Numerical continuation of normally hyperbolic invariant manifolds, Nonlinearity 20 (2007), 1499-1534.
52. HWB and F. Takens, Unicity of KAM tori, Ergod. Th. & Dynam. Sys. 27
(2007), 713-724.
53. HWB, R.H. Cushman, F. Fass`o and F. Takens, Geometry of KAM tori for
nearly integrable Hamiltonian systems, Ergod. Th. & Dynam. Sys. 27
(2007), 725-741.
54. HWB, V. Naudot, R. Roussarie and K. Saleh, Dynamics of a predator-prey
model with non-monotonic response function, DCDS-A 18(2&3) (2007),
221-251.
55. HWB, Computergebruik en demathematisering, Nieuw Arch. Wisk. 5th
series 5(3) (2007), 201-206.
56. HWB, M.C. Ciocci and H. Hanßmann, The quasi-periodic reversible Hopf
bifurcation, IJBC 17(8) (2007), 2605-2623.
57. HWB, V. Naudot, R. Roussarie, K. Saleh and F.O.O. Wagener, Organising
centres in the semi-global analysis of dynamical systems, IJAMAS 12(D07)
(2007), 7-36.
58. HWB, K. Efstathiou and E. Subramanian, Robustness of unstable attractors
in arbitrarily sized pulse-coupled systems with delay, Nonlinearity 21(1)
(2008), 13-49.
59. HWB, K. Efstathiou and E. Subramanian, Heteroclinic cycles between unstable attractors, Nonlinearity 21 (2008), 1385-1410.
19
60. HWB and G. Vegter, Generic Hopf-Neimark-Sacker bifurcations in feed
forward systems, Nonlinearity 21 (2008), 1547-1578.
61. HWB, S.J. Holtman and G. Vegter, Recognition of the bifurcation type of
resonance in mildly degenerate Hopf-Ne˘ımark-Sacker families, Nonlinearity 21 (2008), 2463-2482.
62. HWB, C. Sim´o and R. Vitolo, The Hopf-Saddle-Node bifurcation for fixed
points of 3D-diffeomorphisms, analysis of a resonance ‘bubble’, Physica D
237 (2008), 1773-1799.
63. HWB, C. Sim´o and R. Vitolo, The Hopf-Saddle-Node bifurcation for fixed
points of 3D-diffeomorphisms: the Arnol′ d resonance web, Bull. Belgian
Math. Soc. Simon Stevin 15 (2008), 769-787.
64. HWB and R. Vitolo, Dynamical systems modeling of low-frequency variability in low-order atmospheric models, DCDS-B 10(2/3) (2008) 401-419.
65. Lukina, O.V., F. Takens and HWB, Global properties of integrable Hamiltonian systems, Regular and Chaotic Dynamics 13(6) (2008), 588-630.
66. HWB, M.C. Ciocci, H. Hanßmann and A. Vanderbauwhede, Quasi-periodic
stability of normally resonant tori, Physica D 238 (2009), 309-318
67. HWB, S.J. Holtman, G. Vegter and R. Vitolo, Geometry and dynamics of
mildly degenerate Hopf-Neimarck-Sacker families near resonance. Nonlinearity 22 (2009), 2161-2200.
68. HWB and V.A. Gaiko, Global qualitative analysis of a quartic ecological model. Nonlinear Analysis Series A: Theory, Methods & Applications
(2009): DOI information: 10.1016/j.na.2009.07.004.
69. Sterk, A.E., R. Vitolo, HWB, C. Sim´o and H.A. Dijkstra, New nonlinear
mechanisms of midlatitude atmospheric low-frequency variability. Physica
D: Nonlinear Phenomena 239 (2010), 701-718; DOI information:
10.1016/j.physd.2010.02.003
70. Brandhof, A. van den, HWB and K.P. Hart, Andrei N. Kolmogorov (19031987), bouwer van de kansaxioma’s, Pythagoras 49(5) (2010), 18-23.
71. HWB en K. van der Straaten, Complexe getallen voor Wiskunde D en NLT,
Euclides 85(6) (2010), 239-241.
72. HWB, Do Diophantine vectors form a Cantor bouquet? Journ. Difference
Equations and Applications 16(5,6) (2010) 433-434.
20
73. HWB, C. Sim´o and R. Vitolo, Chaos and quasi-periodicity in diffeomorphisms of the solid torus. DCDS-B 14(3) (2010) 871-905.
74. HWB, S.J. Holtman and G. Vegter, Recognition of resonance type in periodically forced oscillators. Physica D: Nonlinear Phenomena 239(17) (2010)
1627-1636.
75. HWB, K. Efstathiou and O.V. Lukina, A geometric fractional monodromy
theorem. DCDS-S 3(4) (2010) 517-532.
76. R. Vitolo, C. Sim´o, and H.W. Broer, Routes to chaos in the Hopf-saddlenode bifurcation for fixed points of 3D-diffeomorphisms. Nonlinearity 23(8)
1919-1947 DOI: 10.1088/0951-7715/23/8/007
77. HWB, S.J. Holtman, G. Vegter and R. Vitolo, Dynamics and geometry near
resonant bifurcations. Regular and Chaotic Dynamics (on the occasion of
Henk Broer’s 60th birthday) 16(1-2), (2011) 39-50. DOI:
10.1134/S1560354710520023
78. R. Vitolo, HWB, and C. Sim´o, Quasi-periodic Bifurcations of Invariant
Circles in Low-dimensional Dissipative Dynamical Systems. Regular and
Chaotic Dynamics (on the occasion of Henk Broer’s 60th birthday) 16(1-2),
(2011) 154-184. DOI: 10.1134/S1560354710520023
79. HWB, In Memoriam Floris Takens: A total mathematician. Nieuw Archief
Wiskunde 5th series 12(1) (2011) 2024.
80. HWB and S.J. van Strien, In Memoriam Floris Takens 1940-2010. Indag.
Math. 22(3-4) (2011) 137-143.
81. HWB, H.A. Dijkstra, C. Sim´o, A.E. Sterk and R. Vitolo, The dynamics of a
low-order model for the Atlantic Multidecadal Oscillation. DCDS-B 16(1)
(2011) 73-102.
82. D.G.M. Beersma, HWB, K. Efstathiou, K.A. Gargar and I. Hoveijn, Pacer
cell response to periodic Zeitgebers. Physica D 19 (2011) 1516-1527.
83. M.P. Holland, R. Vitolo, P. Rabassa, A.E. Sterk and HWB, Extreme value
laws in dynamical systems under physical observables. Physica D: Nonlinear Phenomena 241 (2012) 497-513; http://dx.doi.org/10.1016/j.physd.2011.11.005.
84. HWB, Resonance and fractal geometry. Acta Applicandæ Mathematicæ
120(1) (2012) 61-86; http://dx.doi.org/10.1007/s10440-012-9670-x.
21
85. HWB, Perspectives on the legacy of Poincar´e in the field of dynamical systems. Nieuw Archief voor Wiskunde 5th series 13(3) (2012) 2012.
86. HWB, M. Levi and C. Sim´o, Large scale radial stability density of Hills
equation. Nonlinearity 26 (2013) 565589.
87. HWB, Bernoulli’s lichtstraal-oplossing van het brachistochrone probleem
door de ogen van Hamilton. Nieuw Archief voor Wiskunde 5th series 14(2)
(2013) 99-107.
88. A.E. Sterk, R. Vitolo and HWB, Het onvoorspelbare venijn van de staart.
Nieuw Archief voor Wiskunde 5th series 14(3) (2013) 164-167.
89. HWB, T.J. Kaper and M. Krupa, Geometric desingularization of a cusp singularity in slow fast systems with applications to Zeemans examples. JDDE
25 (2013) 925-958. doi:10.1007/s10884-013-9322-5
90. K. Efstathiou and HWB, Uncovering fractional monodromy. Comm. Math.
Phys. 324 (2013) 549-588.
91. HWB, Review of ‘Henri Poincar´e: a scientific biography’ by Jeremy Gray.
BSHM Bulletin: Journ. British Soc. Hist. Math. 29(1) (2014) 77-79.
92. H. Jard´on-Kojakhmetov and HWB, Polynomial normal forms of constrained
differential equations with three parameters. Journ. Diff. Eqns. 257(4)
(2014) 1012-1055. doi: 10.1016/j.jde.2014.04.022
93. HWB, Bernoulli’s light ray solution of the brachistochrone problem through
Hamilton’s eyes. IJBC 4(8) (2014) 19 pp.
94. HWB, Near-horizon celestial phenomena, a study in geometric optics. Acta
Applicandæ Mathematicæ (2014). To appear.
95. Xia LIU, K. Efstathiou and HWB, Bifurcations and stability of planar Hopftransversal systems. Preprint University of Groningen, 2011. Submitted.
96. Xia LIU, K. Efstathiou and HWB, A novel regularization of planar Filippov
systems and its applications. In preparation.
97. Lei ZHAO and HWB, De Sitter’s theory of the Galilean satellies and related
quasi-periodic orbits. In preparation.
22
Other publications
1. HWB, Formal normal form theorems for vector fields and some consequences for bifurcations in the volume preserving case. In D. Rand and
L.-S. Young (eds.): Dynamical Systems and Turbulence, Warwick, 1980,
LNM 898, (1981), Springer-Verlag, 54–74.
2. HWB, Quasi-periodic flow near a codimension one singularity of a divergence free vector field in dimension three. In D. Rand and L.-S. Young
(eds.): Dynamical Systems and Turbulence, Warwick, 1980, LNM 898,
(1981), Springer-Verlag, 75–89.
3. HWB and B.L.J. Braaksma, Quasi-periodic flow near a codimension one
singularity of a divergence free vector field in dimension four. In: Bifurcation, Th´eorie Ergodique et Applications (Dijon, 1981), Ast´erisque, 98–99,
(1982), 74–142.
4. HWB and S.J. van Strien, Infinitely many moduli of strong stability in divergence free unfoldings of singularities of vector fields. In J. Palis (ed.): Geometric Dynamics, Proceedings, Rio de Janeiro 1981, LNM 1007, (1983),
Springer-Verlag, 39–59.
5. HWB, Quasi-periodic Hopf-bifurcations in forced oscillations, Proceedings
of the 15th Meeting of the Brasilian Mathematical Society, (1987), 317–328,
IMPA, Rio de Janeiro.
6. HWB, Quasi-periodic bifurcations, applications, Proceedings of the 11th
C.E.D.Y.A. 1989, Universidad de M´alaga (1990), 3–22.
7. HWB, On some quasi-periodic bifurcations. In: Proceedings of the 16th
Meeting of the Brasilian Mathematical Society, (1989), 559-581, IMPA,
Rio de Janeiro.
8. HWB, C. Sim´o and R. Roussarie, A numerical survey on the Takens-Bogdanov
bifurcation for diffeomorphisms. In C. Mira et al (eds.), European Conference on Iteration Theory, 89, World Scientific, Singapore, (1992), 320–334.
9. HWB, Notes on perturbation theory 1991, Erasmus ICP Mathematics and
Fundamental Applications, Aristotle University Thessaloniki, (1993), 44 p.
10. HWB, R. Roussarie and C. Sim´o, On the Bogdanov-Takens bifurcation for
planar diffeomorphisms. In C. Perell´o, C. Sim´o, J. Sol`a–Morales (eds.),
Proceedings Equadiff 91, World Scientific, Singapore, (1993), 81–92.
23
11. HWB, S.-N. Chow, Y. Kim and G. Vegter, The Hamiltonian double-zero
eigenvalue, In: W.F. Langford, W. Nagata (eds.), Normal Forms and Homoclinic Chaos, Waterloo 1992, Fields Institute Communications, 4, (1995),
1–19.
12. HWB. G.B. Huitema and M.B. Sevryuk, Families of quasi–periodic tori in
dynamical systems depending on parameters. In: H.W. Broer, S.A. van
Gils, I. Hoveijn and F. Takens (eds.), Nonlinear Dynamical Systems and
Chaos, Progress in Nonlinear Differential Equations and Their Applications
19, Birkh¨auser Verlag, (1996), 171–212.
13. HWB. H.M. Osinga and G. Vegter, On the computation of normally hyperbolic invariant manifolds. In: H.W. Broer, S.A. van Gils, I. Hoveijn and F.
Takens (eds.), Nonlinear Dynamical Systems and Chaos, Progress in Nonlinear Differential Equations and Their Applications 19, Birkh¨auser Verlag,
(1996), 423–448.
14. HWB, H.M. Osinga and G. Vegter, Computing a normally hyperbolic invariant manifold of saddle type. In: Proceedings of Dynamic Systems &
Applications 2, G.S. Ladde and M. Sambandham (eds.), Dynamic Publishers (Atlanta), (1996), 83-90.
15. HWB, H.M. Osinga and G. Vegter, Computing a normally attracting invariant manifold of a Poincar´e map. In: P.L. Butzer, H. Th. Jongen, W. Oberschelp (eds.) Charlemagne and his Heritage, 1200 years of Civilization and
Science in Europe, BREPOLS (1998), 541-549.
16. HWB and B. Krauskopf, Chaos in periodically driven systems. In B. Krauskopf
and D. Lenstra (eds.), Fundamental Issues of Nonlinear Laser Dynamics,
American Institute of Physics Conference Proceedings 548, (2000), 31-53.
ISBN 1-56396-977-7.
17. HWB and R. Roussarie, Exponential confinement of chaos in the bifurcation set of real analytic diffeomorphisms. In H.W. Broer, B. Krauskopf and
G. Vegter (eds.), Global Analysis of Dynamical Systems, Festschrift dedicated to Floris Takens for his 60th birthday, Bristol and Philadelphia IOP,
2001, 167-210. ISBN 0 7503 0803 6.
18. HWB, A global KAM-Theorem: monodromy in near-integrable perturbations of the spherical pendulum, Proc. ITB 34(2&3) (2003) 309-324.
19. HWB, A. Hagen and G. Vegter, Numerical approximation of normally hyperbolic invariant manifolds, Proceedings of the 4th AIMS Meeting 2002
24
at Wilmington Discrete Contin. Dynam. Systems B, supplemental volume
(2003), 133-140.
20. HWB, R.H. Cushman and F. Fass`o, A Hamiltonian KAM Theorem for bundles of Lagrangean tori. In F. Dumortier, H.W. Broer, J. Mahwin, A. Vanderbauwhede and S.M. Verduyn-Lunel (eds.), Proceedings Equadiff World
Scientific, Singapore, 2005, 696-701
` Jorba, J. Villanueva and F.O.O. Wagener, Quasi21. HWB, H. Hanßmann, A.
periodic response solutions at normal-internal resonances. In: F. Dumortier,
H.W. Broer, J. Mawhin, A. Vanderbauwhede and S.M. Verduyn Lunel (eds.),
Equadiff 2003, Proceedings International Conference on Differential Equations, Hasselt 2003, World Scientific, Singapore, 2005, 702-707. ISBN 981
256 169 2.
22. HWB, J. Hoo and V. Naudot, Normal Linear stability of Quasi-Periodic Tori
in the Hamiltonian 1 : −1 resonance case. In: F. Dumortier, H.W. Broer,
J. Mawhin, A. Vanderbauwhede and S.M. Verduyn Lunel (eds.), Equadiff
2003, Proceedings International Conference on Differential Equations, Hasselt 2003, World Scientific, Singapore, 2005, 708-713. ISBN 981 256 169
2.
23. HWB, V. Naudot and R. Roussarie, Extension of catastrophe theory to
Dulac unfoldings. In: F. Dumortier, H.W. Broer, J. Mawhin, A. Vanderbauwhede and S.M. Verduyn Lunel (eds.), Equadiff 2003, Proceedings International Conference on Differential Equations, Hasselt 2003, World Scientific, Singapore, 2005, 714-719. ISBN 981 256 169 2.
24. HWB, C. Sim´o and R. Vitolo, Quasi-periodic H´enon-like strange attractors in the Lorenz-84 climate model with seasonal forcing. In: F. Dumortier, H.W. Broer, J. Mawhin, A. Vanderbauwhede and S.M. Verduyn
Lunel (eds.), Equadiff 2003, Proceedings International Conference on Differential Equations, Hasselt 2003, World Scientific, Singapore, 2005, 601606. ISBN 981 256 169 2.
25. HWB, M. van Noort and C. Sim´o, Existence and measure of invariant
tori in Hamiltonian one-and-a-half degree of freedom systems. In: F. Dumortier, H.W. Broer, J. Mawhin, A. Vanderbauwhede and S.M. Verduyn
Lunel (eds.), Equadiff 2003, Proceedings International Conference on Differential Equations, Hasselt 2003, World Scientific, Singapore, 2005, 595600. ISBN 981 256 169 2.
25
26. HWB, Quasi-periodicity in dissipative and conservative systems. Proceedings Symposium Henri Poincar´e, Universit´e Libre de Bruxelles 2004, Solvay
Institutes (2005)
http://www.ulb.ac.be/sciences/ptm/pmif/
ProceedingsHP/Proceedings.html
27. HWB, H. Hanßmann, J. Hoo and V. Naudot, Nearly-integrable perturbations of the Lagrange top: applications of KAM theory. In D. Denteneer,
W.Th.F. den Hollander and E. Verbitskiy (eds.), Dynamics and Stochastics
Festschrift in Honor of M. S. Keane IMS Lecture Notes – Monograph Series
48 (2006) 286–303.
28. HWB, M. Golubitsky and G. Vegter, Geometry of resonance tongues. In
D. Ch´eniot, N. Dutertre, C. Murolo, D. Trotman and A. Pichon (eds.), Singularity Theory, Proceedings of the 2005 Marseille Singularity School and
Conference, dedicated to Jean-Paul Brasselet on His 60th Birthday, World
Scientific, 2007, 327-356.
29. HWB, R. van Dijk and R. Vitolo, Survey of strong normal-interenal k : ℓ
resonances in quasi-periodically driven oscillators for ℓ = 1, 2, 3. In G.
Gaeta, R. Vitolo and S. Walcher (eds.), Symmetry and Perturbation Theory,
Proceedings of the International Conference SPT 2007, World Scientific,
2007, 45-55.
30. R. Vitolo, HWB and C. Sim´o, The Hopf-saddle-node for fixed points of 3Ddiffeomorphisms. In G. Gaeta, R. Vitolo and S. Walcher (eds.), Symmetry
and Perturbation Theory, Proceedings of the International Conference SPT
2007, World Scientific, 2007, 280-281.
31. HWB and H. Hanßmann, Perturbation theory (dynamical systems), Scholarpedia, 3(9):2399, 2008.
32. J.M. Aarts and HWB, Schoolmeetkunde in het Horologium Oscillatorium
van Christiaan Huygens. Preprint University of Groningen 2010.
33. HWB, H. Hanßmann and J. You, On the destruction of resonant Lagrangean
tori in Hamiltonian systems. In: A. Johann, H.-P. Kruse, F. Rupp en F.
Schmitz (eds.), Recent Trends in Dynamical Systems, Proceedings of a Conference in Honor of J¨urgen Scheurle, Ch. 13. Springer-Verlag 2013
34. HWB and G. Vegter, Resonance and singularities. In: Santiago Ib´an˜ ez,
´
Jes´us S. P´erez de Rio, Antonio Pumari˜no and J. Angel
Rodr´ıguez (eds.),
Progress and Challenges in Dynamical Systems, Springer Proceedings in
Mathematics & Statistics 54, (2013) 89-126.
26
Books or chapters in books
1. HWB, On some quasi-periodic bifurcations. In: C.P. Bruter, A. Aragnol, A. Lichn´erowicz (eds.): Bifurcation Theory, Mechanics and Physics,
(1983), Reidel, 177-208.
2. HWB and F. Takens, Wegen naar chaos en vreemde aantrekking, een fenomenologische benadering. In: H.W. Broer and F. Verhulst (eds.), Dynamische
Systemen en Chaos, een Revolutie vanuit de Wiskunde, Epsilon-Uitgaven
14, (1990), 1-76.
3. HWB, Introduction to dynamical systems. In: H.W. Broer, F. Dumortier,
S.J. van Strien and F. Takens, Structures in dynamics, finite dimensional deterministic studies, North-Holland (Studies in Mathematical Physics, 1991),
1-23.
4. HWB and F. Dumortier, Genericity and structural stability. In: H.W. Broer,
F. Dumortier, S.J. van Strien and F. Takens, Structures in dynamics, finite
dimensional deterministic studies, North-Holland (Studies in Mathematical
Physics, 1991), 25-52.
5. HWB, A family of quasi-periodic attractors. In: H.W. Broer, F. Dumortier,
S.J. van Strien and F. Takens, Structures in dynamics, finite dimensional deterministic studies, North-Holland (Studies in Mathematical Physics, 1991),
79-96.
6. HWB, Conservative dynamical systems. In: H.W. Broer, F. Dumortier,
S.J. van Strien and F. Takens, Structures in dynamics, finite dimensional deterministic studies, North-Holland (Studies in Mathematical Physics, 1991),
267-302.
7. HWB, J. van de Craats and F. Verhulst, Het einde van de voorspelbaarheid?
Chaostheorie, idee¨en en toepassingen, Aramith Uitgevers – Epsilon Uitgaven 35, 1995; Reprint Chaostheorie – Het einde van de voorspelbaarheid?
Epsilon Uitgaven 35, 2003.
8. HWB and F. Takens, Mathematical aspects of nonlinear dynamical systems, in: Images of SMC Research 1996, Stichting Mathematisch Centrum,
(1996), 179–198.
9. HWB, Meetkunde en fysica, met differentiaalvormen en integraalstellingen,
Epsilon Uitgaven 44, 1999.
27
10. M.C. Ciocci, A. Litvak-Hinenzon and HWB, Survey on dissipative KAM
theory including quasi-periodic bifurcation theory based on lectures by Henk
Broer. In: J. Montaldi and T. Ratiu (eds.): Geometric Mechanics and Symmetry: the Peyresq Lectures, LMS Lecture Notes Series, 306. Cambridge
University Press, 2005, 303-355.
11. HWB, A. Hagen and G. Vegter, A versatile algorithm for computing invariant manifolds. In: A.N. Gorban, N. Kazantzis, I.G. Kevrekidis, H.C.
Oettinger and C. Theodoropoulos (eds.): Model Reduction and CoarseGraining Approaching for Multiscale Phenomena, Springer: Complexity,
Springer-Verlag 2006, 17-38.
12. HWB, Normal forms in perturbation theory. In: R. Meyers (ed.), Encyclopædia of Complexity & System Science. Springer; New York (2009),
6310-6329.
13. HWB and H. Hanßmann, Hamiltonian perturbation theory (and transitions
to chaos). In: R. Meyers (ed.), Encyclopædia of Complexity & System Science. Springer; New York (2009), 4515-4540.
14. HWB and F. Takens, Preliminaries in Dynamical Systems Theory. In: H.W.
Broer, B. Hasselblatt and F. Takens (eds.), Handbook of Dynamical Systems,
Volume 3. North-Holland (2010), 1-42.
15. HWB and M.B. Sevryuk, KAM Theory: quasi-periodicity in dynamical systems. In: H.W. Broer, B. Hasselblatt and F. Takens (eds.), Handbook of
Dynamical Systems, Volume 3. North-Holland (2010), 249-344.
16. HWB and F. Takens, Dynamical Systems and Chaos, Epsilon Uitgaven 64,
2009; Appl. Math. Sciences 172, Springer-Verlag 2011.
17. HWB, Hemelverschijnselen nabij de horizon, naar Minnaert en Wegener,
Bernoulli en Hamilton, Epsilon Uitgaven 77, 2013.
18. HWB, H. Hanßmann and F.O.O. Wagener, Quasi-Periodic Bifurcation Theory, the geometry of KAM (2014, in preparation).
19. HWB, Near horizon celestial phenomena, inspired by Minnaert and Wegener, Bernoulli and Hamilton, MAA Carus-series (to appear).
Editing
20. HWB, B.L.J. Braaksma and F. Takens (eds.), Dynamical Systems and Bifurcations, LNM 1125, (1985), Springer-Verlag.
28
21. HWB and F. Verhulst (eds.), Dynamische systemen en chaos, een revolutie
vanuit de wiskunde, Epsilon-Uitgaven 14, (1990).
22. HWB and F. Takens (eds.), Geometry and analysis in nonlinear dynamics,
Pitman Research Notes in Mathematics Series 222, (1992), Longman.
23. HWB, S.A. van Gils, I. Hoveijn and F. Takens (eds.), Nonlinear Dymamical
Systems and Chaos, Progress in Nonlinear Differential Equations and Their
Applications 19, (1996), Birkh¨auser.
24. HWB, B. Krauskopf and G. Vegter (eds.), Global Analysis of Dynamical
Systems, Festschrift dedicated to Floris Takens for his 60th birthday. Bristol
and Philadelphia IOP, 2001. ISBN 0 7503 0803 6.
25. HWB, F. Dumortier, J. Mawhin, A. Vanderbauwhede and S.M. Verduyn
Lunel (eds.), Equadiff 2003, Proceedings International Conference on Differential Equations, Hasselt 2003, World Scientific, Singapore, 2005. ISBN
981 256 169 2.
26. HWB, B. Hasselblatt and F. Takens (eds.), Handbook of Dynamical Systems
Volume 3. North-Holland, 2010.
Invited lectures and seminars
Conferences and workshops
Some of the meetings listed below are large scale conferences and at many of
those I gave a main address; in the mathematical culture I am from, the notion of
‘key note address’ is less well-known and the closest to that is that of ‘main’ or
‘plenary adress’. Other meetings are smaller scale workshops for experts, where I
always gave a main address. These occassions are indicated in bold face. In both
categories I took part in the organizing committee several times, see section 2
‘Meetings organized’. In the organization of large scale conferences (EQUADIFF
2003, ENOC 2005, indicated in large) I have designed several minisymposia.
- University of Warwick 1980 Bifurcations of singularities in volume preserving vector fields, 1996 Equivariant singularity theory with distinguished
parameters , 2000 KAM Theory in conservative and dissipative systems
- IMPA/UFRJ Rio de Janeiro 1981 Bifurcations of singularities in volume
preserving vector fields, 1985 Infinite modulus of stability in a 3D vector
field, 1987 Real analytic Kupka Smale vector fields, 1989 Parametrised
KAM Theory, 1993 Bifurcational aspects of parametric resonance, 1997 A
normally elliptic Hamiltonian bifurcation, 2000 The fattened Arnol’d family
29
- Universit´e de Bourgogne (Dijon) 1981 Quasi-periodic flow near codimension one singularities of a divergence free 4D vector field
- Forschungsinstitut Oberwolfach 1981 (twice) Bifurcations of singularities
in volume preserving vector fields and Quasi-periodicity in local bifurcation theory, 1983 Subordinate Shilnikov bifurcations in 3D vector fields,
1985 Real analytic Kupka Smale vector fields, 1987 On a quasi-periodic
Hopf bifurcation, 1989 Bifurcational aspects of parametric resonance, 1992
Mixed spectrum and rotational symmetry
- ICTP Tri¨este 1982 Quasi-periodicity in local bifurcation theory, 1984 Infinite modulus of stability in a 3D vector field, 1986 Real analytic Kupka
Smale vector fields, 1988 On a quasi-periodic Hopf bifurcation, 1998 Resonance in Hill’s equation with periodic or quasi-periodic forcing
- Nederlands Wiskundig Genootschap 1981 Bifurcations of singularities in
volume preserving vector fields, 1984 Subordinate Shilnikov bifurcations in
3D vector fields, 1987 On a quasi-periodic Hopf bifurcation, 1995 Geometrical aspects of stability theory for Hill’s equation
- London Mathematical Society (Durham University) 1984 On a quasi-periodic
Hopf bifurcation
- Deutsche Mathematiker Verein, 1984 Subordinate Shilnikov bifurcations in
3D vector fields,
- Workshop Differential Equations, Yale-University 1985 Real analytic Kupka
Smale vector fields
- The Brasilian Mathematical Society, Poc¸os de Caldas 1985 Infinite modulus
of stability in a 3D vector field, IMPA Rio de Janeiro 1987 On a quasiperiodic Hopf bifurcation, 1989 Unfoldings of quasi-periodic tori
- Banach Center Warsaw 1986 On a quasi-periodic Hopf bifurcation
- EQUADIFF Bratislawa 1987 On a quasi-periodic Hopf bifurcation; Barcelona
1991 Formally symmetric normal forms and genericity; Hasselt 2003 A
Hamiltonian KAM Theorem for bundles of Lagrangean tori
- 11th CEDYA, Malaga 1989 Quasi-periodic bifurcations: applications
- LUC Diepenbeek 1992 Bifurcational aspects of parametric resonance
- Woudschoten 1992 Bifurcational aspects of parametric resonance
30
- Fields Institute Waterloo 1992 Bifurcational aspects of parametric resonance, 2011 Resonance and fractal geometry
- EC Program MASIE: 2001 A proof of the iso-energetic KAM Theorem from
the ‘ordinary’ one, 2002 Bifurcational aspects of parametric resonance,
2003 (twice) Geometry of KAM tori in Hamiltonian systems, 2004 Geometry
of resonance tongues
- ENOC Moscow 2003 Geometry of KAM tori in Hamiltonian systems; Eindhoven 2005 KAM Theory: quasi-periodicity in dissipative and conservative systems
- EC-group Pattern Formation, Bilthoven 1993 A normally elliptic Hamiltonian bifurcation; Noordwijkerhout 1994 Unfoldings of quasi-periodic tori
in reversible systems
- Niels Bohr Institutet Copenhagen 1998 Geometry of resonance tongues
- Bressanone 1999 Geometry of resonance tongues
- Heriot-Watt University Edinburgh 2000 Geometry of resonance tongues
- Isaac Newton Institute of Mathematical Sciences Cambridge (UK) 2000
Geometry of resonance tongues
- ITB Bandung 2001 Quasi-periodicity in dissipative systems, 2002 A global
KAM Theorem: monodromy in nearly integrable perturbations of the spherical pendulum, 2005 (EPAM final meeting) KAM Theory: quasi-periodicity
in dissipative and conservative systems
- Morehouse College, Atlanta 2003 On the computation of normally-hyperbolic
invariant manifolds
- Institut Henri Poincar´e, Paris 2003 Geometry of KAM tori in Hamiltonian
systems
- The Catalan Mathematical Society, Barcelona 2003 Kolmogorov: the K of
KAM
- CIRM, Luminy 2004 Geometry of resonance tongues, 2009 Dynamics of a
predator-prey model with non-montonic response function
- International Solvay Institutes, UL-Bruxelles 2004 Quasi-periodicity in dissipative and conservative systems
31
- International Conference on Dynamical Systems, Hsinchu TAIWAN 2005
Quasi-periodicity in dissipative and conservative systems
- SIAM conference Applications of Dynamical Systems, Snowbird UTAH
2005 Quasi-periodicity in dissipative and conservative systems
- International Conference in Ordinary and Partial Differential Equations,
Sevilla 2005 Geometry of resonance tongues
- Symposium in honour of Carles Sim´o’s sixtieth birthday, S. Agaro 2006
Low frequency variation in climate models: a dynamical systems perspective
- Symposium in honour of KNMI director Gerbrand Komen, Utrecht University 2006 Low-frequency climate variability: a dynamical systems approach
- Conference in honour of Richard Cushman’s sixty fifth birthday, Utrecht
2007 Geometry of resonance tongues
- Conference Dynamics in Perturbations in honour of Freddy Dumortier’s
sixtieth birthday, Diepenbeek-Brussels 2007 Multiperiodic dynamics: an
overview and some recent results
- Conference Symmetry and Perturbation Theory, Otranto 2007 Multiperiodic dynamics: an overview and some recent results; 2011 Resonance
and fractal geometry
- Workshop Hamiltonian Lattice Dynamical Systems, Lorentz Center 2007
On parametrized KAM Theory
- Workshop Dynamics and Topology, Tossa de Mar 2008 On parametrized
KAM Theory
- Dynamics Days TUDelft 2008
- Workshop Monodromy and Geometric Phases, Lorentz Center (Leiden University) 2009, KAM Theory: multiperiodicity in conservative and dissipative systems
- Workshop Mathematical Control Theory and Mechanics, Russian Academy
of Sciences 2009, Multiperiodic dynamics: an overview and some recent
results
- South-East AMS Meeting in Boca Raton 2009 Multiperiodic dynamics: an
overview and some recent results
32
- Workshop (connected to) winter school Evolution Equations in an Applied
Context, December 2010 at University of Twente, Resonance and Fractal
Geometry
- AIMS Conference on Dynamical Systems, Differential Equations and Applications 24-26 May 2010 On Parametrized KAM Theory
- Workshop ‘Hamiltonian Dynamics and Celestial Mechanics 2011’ on behalf of Ken Meijers 75th birthday, May 2011. Resonance and Fractal
Geometry
- Workshop ‘Symmetry and Perturbation Theory’ Otranto June 2011. Resonance and Fractal Geometry
- Workshop ‘Instabilities in Hamiltonian Systems’ Fields Institute Toronto
June 2011. Resonance and Fractal Geometry
- Workshop ‘Recent trends in dynamical systems’ TU-M¨unchen 2012. Resonance and Fractal Geometry
- Conference ‘100 years after Poincar´e’, Universidad de Oviedo 2012. Resonance and Fractal Geometry
- Henri Poincar´e Centennial Symposium, Utrecht University 2012.
- Jan van Mill Symposium, VUA 2012. Bernoulli’s lightray solution for
the brachistochrone problem from Hamilton’s viewpoint
- Univerity of Colorado at Boulder (Jim Meiss 60) 2014. Near-horizon celestial phenomena, inspired by Minnaert and Wegener, Bernoulli and Hamilton
- Lobatchevsky State University of Nizhniy Novgorod 2014. Two conferences, four lectures:
Near-horizon celestial phenomena, inspired by Minnaert and Wegener, Bernoulli
and Hamilton,
Resonance and Fractal Geometry (both opening address)
and two course lectures Parametrized KAM Theory
- Scientific Meeting Mathematical Physics (FOM) 1995 Mixed spectrum and
rotational symmetry, 1997 Invariant circles in the Bogdanov-Takens bifurcation for diffeomorphisms, 1999 Quasi-periodicity in dissipative and conservative systems, 2000 The how and what of chaos, 2001 Geometry of resonance tongues: a Singularity Theory approach, 2003 Geometry of KAM
tori in nearly integrable Hamiltonian systems
33
- International School of Philosophy Leusden 1987 Chaos in 1D maps
Colloquia and seminars
- Boston University 1985, 1986, 1991, 1994, 1995, 1999, 2003, 2004, 2006,
2009
- Brown University and Michigan State University 1985, 1986
- IMPA/UFRJ Rio de Janeiro 1987
- Universit´e de Bourgogne (Dijon) 1987, 1990, 1997, 1999, 2000, 2003, 2004
- Limburgs Universitair Centrum Diepenbeek / Hasselt 1988, 1998
- Universitat de Barcelona (and Universitat Aut´onoma de Barcelona) 1989,
1990, 1991, 1997, 1997, 1998, 1999, 2003 (twice), 2004, 2005, 2006, 2008,
2009, 2010, 2011, 2012
- IMA Minneapolis 1990, 1997
- Georgia Institute of Technology Atlanta 1991, 1995, 1998, 2003
- University of Houston 1991, 2000, 2003, 2004
- IMPA / UFRJ Rio de Janeiro 1987, 1989, 1993, 1997
- University of Campinas (Brazil) 1987
- RWTH Aachen 1990, 1995, 1998 (Graduiertenkolleg)
- Universities of Augsburg and M¨unchen 1990
- University of Stuttgart 1991
- Rensselaer Polytechnic Institute 1994
- LUC Diepenbeek 1988, 1998
- Pennsylvania and Indiana State Universities 1999, 2006
- University of Padua 2000
- University of Bristol and Imperial College London 2003
- Heriot–Watt University at Edinburgh 2006
34
- Carl von Ossietzky Universit¨at Oldenburg 2009
- Universit´e de Nice Sophia-Antipolis 2011
- Staff-colloquia / -seminars at (Polytechnical) Universities in the Netherlands: Utrecht (1981, 1988 (seminar Applied Analysis), 1990, 2000, 2003,
2006, 2008), Leiden (1990), University of Amsterdam (1988, 1994), VUA
(1980, 1985 (Applied Analysis), 1997, 2005, 2012, 2012), Delft (1987
(Applied Analysis)), Twente (1985, 1986, 1990, 1999, 2000, 2011), Eindhoven (2000, 2007), Groningen (2011)
- Lezing Huygens’ isochrone slinger
VU en TUDelft W&I Studievereniging Christiaan Huygens (1999-2000)
Museum Hofwijck Christiaan Huygens Lezing (2001)
- Lezingen Kansrekening en Statistiek, Wiskunde D-middag, Scholieren Academie,
Rijksuniversiteit Groningen, Mei 2008
Kepler’s Derde Wet en de Stabiliteit van het Zonnestelsel, Wiskunde D-dag,
Hogeschool Domstad, Juni 2008
Determinisme, Chaos en Toeval, Masterclass VWO, Rijksuniversiteit Groningen, April 2010
- Lezing Resonance and Fractal Geometry, KNAW afdeling Natuurkunde
(Mei 2010), UTwente (December 2010), RUGroningen (February 2011)
- Lezing Huygens and Bernoulli’s Brachistochrone, Afscheid Henk de Snoo,
December 2010; E´en Dag Student RuG, March 2011
Often visiting positions of one Month or longer were held at the various institutions, this apart from many shorter visits. I like to mention University of Warwick 1981 (six weeks, funded by NWO), Boston University 1985 (visiting professorship of one semester), Limburgs Universitair Centrum Diepenbeek 1988 and
1992 (two Months twice), IMPA/UFRJ (Rio de Janeiro) 1985, 1987, 1989, 1993,
Universit´e de Bourgogne 1987 and 2004-2005 (twice one Month), Universitat de
Barcelona 1997 (totally one Month), 1998, 2000, 2002, 2003 (four times one
Month), Universit´e de Nice (2011)
General statement of research interest
My research area is Nonlinear Dynamical Systems, both fundamental and applied aspects included, that provenly cross fertilise each other. Mathematically
35
speaking Nonlinear Dynamical Systems overlaps with more classical disciplines
as Mathematical Analysis, Geometry (Topology), Measure Theory and Numerical Mathematics. This interaction between various subdisciplines always has been
fascinating to me. Application areas include topics in Mathematical Physics and
in the modelling of Earth- and Life Sciences. The latter tendency over the last five
years has been increased by the existence of the NWO-cluster Nonlinear Dynamics of Natural Sciences, of which Groningen has become the center. See Section
4 ‘Grant support’ for further details. The group maintains a large national and
international network for research cooperation.
Overall goal is the advancement and renovation of the state-of-the-art in the field,
where the knowledge is disseminated by publications in highly ranking journals
and by lectures at international conferences and workshops. From my CV it may
be clear that we are often succesful in both of these respects. Also in the PhD
juries (leescommissies) we often succeed to include well-known international experts.
Dynamical Systems Theory
A general background problem is to develop a mathematical language for describing long-term dynamical behaviour. Distinguishing asymptotic equilibrium
dynamics, periodicity, multi- or quasi-periodicity and chaos, one major goal is
to understand the possible transitions (or bifurcations) between such states when
system parameters (modelling external circumstances) are changing. In particular
the focus then is on transitions from simple to complex dynamics. Here (multi-)
periodicity acts as ‘order amidst chaos’. In this tradition there are several ongoing,
interconnected subprograms with great challenges and with a strong international
embedding. We now give a more detailed discussion.
KAM Theory. A main part of the program deals with the persistent occurrence
of quasi-periodicity in dynamical systems, as this is confined to invariant tori.
Study of this kind of motion has a long tradition in the Solar System, for instance
when considering Sun and Moon in the prediction of eclipses. We here contribute
to Kolmogorov-Arnold-Moser (or KAM) Theory, which studies the persistence of
these tori in perturbations of so-called integrable systems. A number of classical
examples fit in this integrable category, as well as approximations (truncations) of
generic systems, e.g., at equilibria or at periodic solutions. We deal with perturbations of such integrable systems, where the convergence of certain perturbation
series is hampered by a dense set of resonances.
The Groningen contribution to this field is the Parametrized KAM Theory, which
is a marriage of KAM Theory and Singularity Theory. This program was ini-
36
tiated in cooperation with Boele Braaksma during the 1980’s and the theses of
George Huitema (NWO), Heinz Hanßmann, Florian Wagener (NWO), Hans de
Jong (FOM), Jun Hoo (FOM) and Maria Cristina Ciocci (Ghent) were in this
line, see Section 3 on ‘PhD supervision’ of the CV. A number of these students are still cooperating with the group, as do the professors emeriti Richard
Cushman (UU) and Ferdinand Verhulst (UU). Also I regularly meet with ex`
perts like Luigi Chierchia (Roma Tre), Angel
Jorba (Universitat de Barcelona),
Amadeu Delshams (Universitat Polit`ecnica de Catalunya), Mikhail Sevryuk (Russian Academy of Sciences, Moskou), Yingfei Yi (Georgia Institute of Technology, Atlanta), Sergei Kuksin (Heriott Watt University, Edinburgh), J¨urgen P¨oschel
(Universit¨at Stuttgart), H´akon Eliasson (Universit´e Paris VII) and Rafael de la
Llave (University of Texas, Austin). Quite a number of them were present at the
Lorentz Center workshops KAM Theory and its applications, organized by me in
cooperation with Hanßmann and Sevryuk, December 2008, see Section 2.
One KAM project deals with quasi-periodic bifurcations, both in the general ‘dissipative’ setting and in the conservative and other settings. The dissipative part
of the theory has significance for the onset of turbulence as initiated by HopfLandau-Lifschitz-Ruelle-Takens in the 1940’s-70’s. In general it provides scenario’s for increasing complexity in the dynamics in dependence of parameter
variation and when the dimension of the state space gets larger. This theory also
is of importance for modelling in infinite dimensional dynamical systems, like
in certain PDE’s, delay equations, etc. There is ongoing research in this direction, which also provides a clear link with other members of the NWO-cluster
NDNS+, which in turn enhances further exploration in the future. Recently a
textbook Dynamical Systems and Chaos appeared, authored by me in cooperation
with Takens, that explains many mathematical background ideas. Also I refer to
the workshop New Direction in Dynamical Systems, organized by me in cooperation with Hanßmann, Homburg, Huitema and Van Strien, December 2009, again
see Section 2.
A second KAM project takes place in the conservative setting. Here (near-) integrability traditionally is part of the modelling in Classical Mechanics. One ‘modern’,
geometrical aspect is the non-triviality of Lagrangean torus bundles which turns
out to be of importance for the occurrence of quantum monodromy and spectral
defects. In cooperation with Takens, Cushman (Calgary) and Francesco Fasso
(Padua), recently an innovative result on Cantorised torus bundles has been obtained, for which a global version of KAM Theory had to be developed. In this
research area there are quite a few new challenges and also the junior reseachers
Konstantinos Efstathiou and Olga Lukina are involved in this. Lukina defended
her thesis September 2008, see Sections 3 and 4. One clear target concerns the
classification of symplectic torus bundles and their possible occurrences in Hamiltonian systems. Another target tries to understand more or less physical invariants
37
like fractional monodromy or bidromy in terms of the geometrical language of
dynamical systems. One important tool turns out to be the covering space. An
open problem aims to extend the existing connection between classical and quantum monodromy for integrable systems, to nearly integrable systems. In 2007
the group in this direction got reinforced by Holger Waalkens as a tenure track
professor. On this subject there is collaboration with Boris Zhilinski´ı and Dmitri
Sadovski´ı from Dunkerque.
Resonance. Another part of the program deals with resonance, which to some
extent is complementary to the multi-periodic KAM part. Resonance is the dynamical interaction ‘at low integers’ of several oscillating subsystems, leading to
periodic motions; of which synchronisation is one example. Usually a number
of parameters play a role, e.g., for detuning the resonance or for controlling the
strength of the interaction. In the mathematical formulation we often look for
generic, universal models, that are independent of the specific context. Here the
methods of Singularity Theory can be frequently applied that lead to universal
geometry in the product of state space and parameter space. The PhD theses of
Bernd Krauskopf, Gerton Lunter, Martijn van Noort (NWO) and Sijbo Holtman
(NWO), see Section 3.
The resonance program is branched over several projects, one of which deals with
degenerate Hopf-Ne˘ımark-Sacker bifurcations, in cooperation with Gert Vegter
and Martin Golubitsky (Houston) and supported by the PhD research of SijboJan Holtman (NWO), see Sections 3 and 4. A second project, in the conservative
setting, deals with the Hill-Schr¨odinger equation with (quasi-) periodic forcing or
potential. This turns out to be relevant for a corresponding Schr¨odinger operator,
where we develop a theory for generic gap-closing. This is joint work with Mark
Levi (Penn State University), Carles Sim´o (Universitat de Barcelona) and Joaquim
Puig (Universitat Polit`ecnica de Catalunya), see Section 3 on PhD Examination.
In both projects several papers have been published already and several others are
in press and in preparation. One ongoing project concerns the geometry of resonance tongues in degenerate Hopf-Ne˘ımark-Sacker bifurcations also in coupled
cell systems. Another project deals with the large scale stability properties in the
parameter space of Mathieu’s equation.
Applications
In Groningen traditionally there has been a lot of interest in applications, in particular in modelling and simulation. Interpretation of the computer output, keeping
track of the most recent theoretical developments, is one of our main objectives.
Apart from the applications in Mathematical Physics described earlier, we en-
38
joy an increasing interest in Earth- and Life Sciences. This fits very well in the
NDNS+ cluster plans.
Climate modelling. A long term applied project in the context of climate variability in 1998 started with the PhD research of Vitolo, again see Section 4. This
research was based on the Lorenz-84 model, developed by Edward Lorenz in
1984. Roughly during the same time, two PhD theses in this direction were written at the UU under Ferdinand Verhulst and Theo Opsteegh (UU, KNMI, IMAU).
The models related to Lorenz-84 are obtained by truncating an infinite dimensional PDE model by a so-called Galerkin projection, so to end up with a finite
dimensional dynamical system. This approximation describes the low frequency
motion of the system.
All these efforts give evidence that a climate variability of around 50 years, called
Atlantic Multidecadal Oscillation (AMO), may very well be related to a specific
dynamical feature called ‘heteroclinic cycle’. Understanding the physics of the
AMO is of importance for the detection of climate changes due to greenhouse
gasses in the atmosphere. This raises novel and exciting dynamical questions
which were picked up in cooperation with Henk Dijkstra (IMAU), Carles Sim´o
(Barcelona) and the former PhD student Renato Vitolo (Exeter). In a corresponding NWO (ALW) project Alef Sterk has finished his PhD research recently, see
Sections 3 and 4.
Since 2011 a Complexity NET European network PREDEX has started to understand extreme values in weather and climate evolution, with Renato Vitolo
(Exeter) as PI. Both Exeter and Groningen are awarded a postdoc, each payed by
the national research foundation. In Groningen Pau Rabassa has been appointed
and in Exeter Alef Sterk. The Groningen programme focusses on chaotic systems in low dimension to develop the appropriate statistical theory. Mark Holland
(Exeter) is a partner in this.
Dynamics of Life Sciences. Another line of modelling started in 2001 with the
PhD work of Khairul Saleh (KNAW), see Section 4 ‘Grant Support’. The ideas
were applied to a predator prey model with non-monotonic response function.
This research was supported by Vincent Naudot (Warwick), Robert Roussarie
(Dijon) and Jean-Christophe Poggiale (Marseille). In the PhD project of Easwar
Subramanian (see Sections 3 and 4) we started working on the visual neurocortex,
in joint supervision with Nicolai Petkov. The defence took place in 2008. This
research mathematically leads to the setting of coupled cell networks, where at
each cell an oscillator is situated. The long term goal is to get insight in what the
coupled cell network modelling can contribute to the understanding of the cortical
physics. Two papers in the journal Nonlinearity developed and applied the con39
cept of unstable attractor and corresponding heteroclinic cycles, also discussing
their role in the neurocortex setting. Here we cooperate with Marc Timme (Max
Planck Institute G¨ottingen) and Martin Golubitsky (Houston).
Also contacts for dynamical systems modelling within the University of Groningen are being established with the group Chronobiology under Domien Beersma.
In the former case we just finised a paper on pacer cells, in cooperation with Kim
Cargar, Konstantinos Efstathiou and Igor Hoveijn (Groningen). We are planning
a Lorentz Center workshop on Resonance and Synchronization in 2012.
Control theory. There is an ongoing collaboration with the Engineering Mechanics group of Henk Nijmeijer of the TU/e. We have an NWO project Stability
and stabilisation of invariant sets in differential inclusions, funded by the Applied
Mathematiscs section of Exact Sciences, see Sections 3 and 4. Two PhD students
are at work here, the Groningen counterpart of which is played by Mrs. Xia Liu.
In this project interesting new challenges are met in the theoretical development
around discontinuities in both dynamics and bifurcation sets.
Conclusion
A number of challenging theoretical problems, in close connection with the above,
arise in the interaction of several subfields. These fields are situated both within
mathematics and within the application areas. This cross fertilization between
theory and applications is a distinctive feature for the Groningen research in Dynamical Systems. Three main theoretical and ongoing themes arise in the context
of parametrized systems, undergoing all kinds of bifurcations (or phase transitions) upon variation of the parameters. All themes have a thorough national and
international embedding, for details see above.
The first theme deals with the universal geometries structuring generic dynamical
systems, mostly in dependence of parameters. Usually the corresponding results
use Singularity Theory in the mathematical background, where the focus of the
applications is formed by various resonance phenomena. See above. Here there
is a long standing collaboration with Vegter, including PhD research of Lunter,
Van Noort and Holtman, see Sections 3 and 4. Recently the attention also goes
to cases of higher dimensional systems, which is of importance for more modern
forms of modelling.
The second theme concerns the various transitions of multi- or quasi-periodic tori,
as well as their global geometry in the phase space. See above for the link with
classical and quantum monodromy. This theme uses Differential Geometry and
Algebraic Topology on the one hand, and Kolmogorov-Arnold-Moser (KAM) Theory on the other hand. Here a full understanding of the parameter dependence also
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involves the first theme. Regarding multi-periodic tori a large part of this research
was developed around the PhD research of Huitema, Hanßmann, Wagener, Vitolo,
Hoo, Lukina and Liu, see Sections 3 and 4.
The third theme concerns the understanding and characterisation of chaos and
strange attractors of which in low dimensions much more is known than in higher
dimensions. Nevertheless, for these higher dimensions, often much can be guessed
from numerical experiments. This often leads to innovative, ‘experimental’ mathematics, where the initial motivation comes from simulation of models. See
above. Several contributions in this direction have been and are still being developed around the PhD research of Wagener, Van Noort, Vitolo, Sterk and Rabassa.
Compare Sections 3 and 4.
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