Communicating the results of my research
Doing research as a mathematician means spending a lot of time on the precise formulation of the problems you want to attack, and then hopefully find a conclusive answer to these problems, or at least a useful procedure or method which may lead to an answer. Finally one has to communicate the outcome of this research to the colleagues, in order to get their approval. This communication process essentially follows two different paths, one by giving talks at conferences and universities, the other one by writing papers and get them published in journals or conference proceedings. On this page you find the results of my writing and publication efforts.

Books (and chapters in books)

• Continuation of Periodic Orbits in Symmetric Hamiltonian Systems
  J. Galán-Vioque and A. Vanderbauwhede
  Numerical Continuation Methods for Dynamical Systems
  Path following and bounday value problems
  B. Krauskopf, H. Osinga and J. Galán-Vioque (Eds.)
  Springer Series in Understanding Complex Systems
  Springer Verlag (2007) 269-299


• Trends in Dynamical Systems
  Proceedings Contactforum, Brussels 17 March 2006
  F. Dumortier, D. Roose and A. Vanderbauwhede(Eds.)
  Handelingen van de Koninklijke Vlaamse Academie van België voor Wetenschappen en Kunsten, 2007


• Equadiff 2003 - Proceedings of the International Conference on Differential Equations
  Hasselt, Belgium, July 22-26, 2003
  F. Dumortier, H. Broer, J. Mawhin, A. Vanderbauwhede and S. Verduyn Lunel (Eds.)
  World Scientific Publishing Co., 2005, 1184 p.


• Center Manifold Theory in Infinite Dimensions
  A. Vanderbauwhede and G. Iooss
  Dynamics Reported - New Series Vol. 1
  C. Jones, U. Kirchgraber & H.O. Walther (Eds.)
  Springer Verlag (1992) 125-163


• Centre Manifolds, Normal Forms and Elementary Bifurcations
  A. Vanderbauwhede
  Dynamics Reported, Volume 2
  U. Kirchgraber and H.O. Walther (Eds.)
  John Wiley & Sons Ltd and B.G. Teubner (1989) 89-169


• Local Bifurcation and Symmetry
  A. Vanderbauwhede
  Research Notes in Mathematics, vol. 75, Pitman, London, 1982, 350 p.

Work in progress

The publications on which I am working for the moment can be found here.

Recent publications

• Continuation and bifurcation of multi-symmetric solutions in reversible Hamiltonian systems
  A. Vanderbauwhede
  Discrete and Continuous Dynamical Systems Series A 33 (2013) 359-363
  


• Local invariant manifolds and normal forms
  F. Takens and A. Vanderbauwhede
  Handbook of Dynamical Systems, Volume 3
  H.W. Broer, B. Hasselblatt and F. Takens (Eds.)
  Elsevier (2010) 89-124
  


• Lyapunov-Schmidt - A Discrete Revision
  A. Vanderbauwhede
  Discrete Dynamics and Difference Equations
  Proceedings of the ICDEA 2007 Conference, Lisbon 2007
  S. Elaydi, H. Oliveira, J.M. Ferreira and J.F. Alves (Eds.)
  World Scientific (2010) 120-143
  


• Subharmonic bifurcation from relative equilibria in reversible systems with rotation symmetry
  A. Vanderbauwhede
  Advances in Discrete Dynamical Systems
  S. Elaydi, K. Nishimura, M. Shishikura and N. Tose (Eds.)
  Advanced Studies in Pure Mathematics Vol. 53
  Mathematical Society of Japan (2009) 371-385
  Preprint


• Lyapunov-Schmidt Method for Dynamical Systems
  A. Vanderbauwhede
  Encyclopedia of Complexity and System Science
  Robert A. Meyers (Ed.)
  Springer, New York (2009) 5299-5315
  Online at Springerlink.com


• Change of stability without bifurcation: an example
  F.J. Muñoz Almaraz, E. Freire, J. Galán and A. Vanderbauwhede
  Difference Equations and Applications
  Proceedings of the ICDEA 2008 Conference, Istanbul 2008
  M. Bohner, Z. Došlá, G. Ladas, M. Ünal and A. Zafer (Eds.)
  Bahçeşehir University Publications (2009) 3-18.
  Preprint


• Quasi-periodic stability of normally resonant tori
  H.W. Broer, M.C. Ciocci, H. Hanßmann and A. Vanderbauwhede
  Physica D 238 (2009) 309-318
  PDF-version


• Continuation of periodic solutions in conservative and reversible systems
  A. Vanderbauwhede
  Symmetry and Perturbation Theory
  Proceedings of the Conference SPT2007, Otranto, 2007
  G. Gaeta, R. Vitolo and S. Walcher (Eds.)
  World Scientific (2007) 198-205
  PDF-version


• Continuation of Gerver's supereight choreography
  F.J. Muñoz-Almaraz, E. Freire, J. Galán-Vioque and A. Vanderbauwhede
  Monografías de la Real Academia de Ciencias de Zaragoza 30 (2006) 95-105
  PDF-version


• Elemental Periodic Orbits associated with the Libration Points in the Circular Restricted 3-Body Problem
  E.J. Doedel, V. Romanov, R.C. Paffenroth, H.B. Keller, D.J. Dichmann, J. Galán-Vioque and A. Vanderbauwhede
  International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 17 (2007) 2625-2677


• Continuation of normal doubly symmetric orbits in conservative reversible systems
  F.J. Muñoz-Almaraz, E. Freire, J. Galán-Vioque and A. Vanderbauwhede
  Celestial Mechanics and Dynamical Astronomy 97 (2007) 17-47


• Pierre-François Verhulst's Final Triumph
  J. Kint, D. Constales and A. Vanderbauwhede
  The Logistic Map and the Route to Chaos
  M. Ausloos and M. Dirickx (Eds.)
  Springer UCS Series, 2006, 13-28


• Elemental periodic orbits of the CR3BP: a brief selection of computational results
  E.J. Doedel, D.J. Dichmann, J. Galán-Vioque, H.B. Keller, R.C. Paffenroth and A. Vanderbauwhede
  Equadiff 2003 - Proceedings Int. Conf. on Differential Equations
  Hasselt 2003
  F. Dumortier, H. Broer, J. Mawhin, A. Vanderbauwhede and S. Verduyn Lunel (Eds.)
  World Scientific Publishing Co. 2005, 163-168


• Bifurcation of Periodic Points in Reversible Diffeomorphisms
  M.-C. Ciocci and A. Vanderbauwhede
  New Progress in Difference Equations - Proceedings ICDEA2001, Augsburg
  S. Elaydi, G. Ladas and B. Aulbach (Eds.)
  Chapman & Hall, CRC Press (2004) 75-93


• Continuation of periodic orbits in conservative and Hamiltonian systems
  F.J. Muñoz-Almaraz, E. Freire, J. Galán, E.J. Doedel and A. Vanderbauwhede
  Physica D 181 (2003) 1-38


• Continuation of periodic solutions in conservative systems with application to the 3-Body problem
  E.J. Doedel, R.C. Paffenroth, H.B. Keller, D.J. Dichmann, J. Galán and A. Vanderbauwhede
  Int. J. Bifurcation and Chaos, 13 (2003) 1353-1381


• Branches of invariant tori and rotation numbers in symmetric Hamiltonian systems: an example
  F.J. Muñoz-Almaraz, E. Freire, J. Galán and A. Vanderbauwhede
  Symmetry and Perturbation Theory - Proceedings of SPT2002
  S. Abenda, G. Gaeta and S. Walcher (Eds)
  World Scientific, Singapore, 2003, 267-276


• Stability and Bifurcations of the Figure-8 Solution of the Three-Body Problem
  J. Galán, F.J. Muñoz-Almaraz, E. Freire, E. Doedel and A. Vanderbauwhede
  Phys. Rev. Lett. 88 (2002) 241101


• Continuación de órbitas periódicas en sistemas Hamiltonianos con simetría: aplicación a mecánica celeste
  J. Galán, F.-J. Muñoz-Almaraz, E. Freire, E.J. Doedel and A. Vanderbauwhede
  Actas XVII Cedya Congreso de Ecuaciones Diferenciales y Aplicaciones
  Salamanca, Septiembre 2001, 8 pp.


• An example of symmetry reduction in Hamiltonian systems
  A. Vanderbauwhede
  International Conference on Differential Equations, Berlin 1999
  B. Fiedler, K. Groger and J. Sprekels (Eds)
  World Scientific, Singapore, 2000, 210-212


• Subharmonic bifurcation at multiple resonances
  A. Vanderbauwhede
  Proceedings of the Mathematics Conference (Birzeit, August 1998)
  S. Elaydi, F. Allen, A. Elkhader, T. Mughrabi and M. Saleh (Eds)
  World Scientific, Singapore, 2000, 254-276


• On the bifurcation and stability of periodic orbits in reversible and symplectic diffeomorphisms
  M.C. Ciocci and A. Vanderbauwhede
  Symmetry and Perturbation Theory - Proceedings of SPT98
  A. Degasparis and G. Gaeta (Eds.)
  World Scientific, 1999, 159-166


• Branching of Periodic Orbits in Hamiltonian and Reversible Systems
  A. Vanderbauwhede
  Proceedings Equadiff 9 (Brno 1997)
  R.P. Agarwal, F. Neuman and J. Vosmansky (Eds.)
  Masaryk University, Brno (1998) 169-181


• Bifurcation of Periodic Orbits for Symplectic Mappings
  M.-C. Ciocci and A. Vanderbauwhede
  Journal of Difference Equations and Applications 3 (1998) 485-500

Older publications

Publications which appeared before 1998 can be found on a separate page.

Unpublished Preprints

• A short tutorial on Hamiltonian systems and their reduction near a periodic orbit
  A. Vanderbauwhede
  Preprint University of Gent (1997) 23 p.
  PDF-version


• Hopf bifurcation at k-fold resonances in reversible systems
  J. Knobloch and A. Vanderbauwhede
  Preprint M 16/95, Technical University of Ilmenau (1995) 21 p.
  PDF-version

Popularizing Articles
These publications are all in Dutch.

• Chaosleer: een wetenschappelijke revolutie?
  VeLeWe Congresboek 1990
  Uitgeverij de Sikkel, Antwerpen (1990) 7-26


• Deterministische Chaos
  Nieuwe visies in de wetenschap
  J. Kint (Red.)
  Acco, Leuven en Amersfoort (1989) 11-42


• Deterministische chaos:
  van Henri Poincaré tot Mitchell Feigenbaum
  Determinisme, chaos, orde, vrijheid?
  Proceedings Symposium "Nieuwe visies in de wetenschap"
  Rijksuniversiteit Gent (1988) 10-22