Dynamics, Bifurcation and Symmetry

1. Front Matter

   Pages i-xv

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2. A Spatial Center Manifold Approach to a Hydrodynamical Problem with O(2) Symmetry

   • Andrei Afendikov, Alexander Mielke

   Pages 1-10

3. Analyzing Bifurcations in the Kolmogorov Flow Equations

   • D. Armbruster, B. Nicolaenko, N. Smaoui, P. Chossat

   Pages 11-33

4. Oscillator Networks with the Symmetry of the Unit Quaternion Group

   • Peter Ashwin, Gerhard Dangelmayr, Ian Stewart, Michael Wegelin

   Pages 35-48

5. An Investigation of a Mode Interaction Involving Period-Doubling and Symmetry-Breaking Bifurcations

   • P. J. Aston

   Pages 49-58

6. Sets, Lines and Adding Machines

   • Jorge Buescu, Ian Stewart

   Pages 59-68

7. Mixed-Mode Solutions in Mode Interaction Problems with Symmetry

   • Sofia Castro

   Pages 69-77

8. A Classification of 2-Modes Interactions with SO(3) Symmetry and Applications

   • Pascal Chossat, Frederic Guyard

   Pages 79-95

9. Non Linear Parabolic Evolutions in Unbounded Domains

   • P. Collet

   Pages 97-104

10. Eigenvalue Movement for a Class of Reversible Hamiltonian Systems with Three Degrees of Freedom

    • Michael Dellnitz, Jürgen Scheurle

    Pages 105-110

11. Blowing-Up in Equivariant Bifurcation Theory

    • Mike Field

    Pages 111-122

12. A Remark on the Detection of Symmetry of Attractors

    • Karin Gatermann

    Pages 123-125

13. Coupled Cells: Wreath Products and Direct Products

    • Martin Golubitsky, Ian Stewart, Benoit Dionne

    Pages 127-138

14. Hopf Bifurcations on Generalized Rectangles with Neumann Boundary Conditions

    • Gabriela Gomes, Ian Stewart

    Pages 139-158

15. The Role of Geometry in Computational Dynamics

    • John Guckenheimer

    Pages 159-165

16. Hopf Bifurcation at k-Fold Resonances in Equivariant Reversible Systems*

    • Jürgen Knobloch, Andre Vanderbauwhede

    Pages 167-179

17. Symmetries and Reversing Symmetries in Kicked Systems

    • Jeroen S. W. Lamb, Hanna Brands

    Pages 181-196

18. Exclusion of Relative Equilibria

    • Reiner Lauterbach, Pascal Chossat

    Pages 197-203

19. Bifurcation of Periodic Orbits in 1:2 Resonance: A Singularity Theory Approach

    • Victor G. Leblanc, William F. Langford

    Pages 205-219

20. Hamiltonian Structure of the Reversible Nonsemisimple 1:1 Resonance

    • J. C. van der Meer, J. A. Sanders, A. Vanderbauwhede

    Pages 221-240

This book collects contributions to the conference" Dynamics, Bifurcation and Symmetry, new trends and new tools", which was held at the Institut d'Etudes Sci­ entifiques de Cargese (France), September 3-9, 1993. The first aim of this conference was to gather and summarize the work of the European Bifurcation Theory Group after two years of existence (the EBTG links european laboratories in five countries via an EC grant). Thanks to a NATO ARW grant, the conference developed into an international meeting on bifurcation theory and dynamical systems, with the partic­ ipation of leading specialists not only from Europe but also from overseas countries (Canada, USA, South America). It was a great satisfaction to notice the active, and quite enthusiastic participation of many young scientists. This is reflected in the present book for which many contributors are PhD students or post-doc researchers. Although several "big" themes (bifurcation with symmetry, low dimensional dynam­ ics, dynamics in EDP's, applications, . . . ) are present in these proceedings, we have divided the book into corresponding parts. In fact these themes overlap in most contributions, which seems to reflect a general tendancy in nonlinear science. I am very pleased to thank for their support the NATO International Exchange Scientific Program as well as the EEC Science Program, which made possible the suc­ cess of this conference.

• applied mathematics
• bifurcation
• computation
• dynamical systems
• form
• manifold
• mathematics
• online
• pattern
• symmetry
• tool
• ordinary differential equations

• Institut Non Linéaire de Nice, CNRS — Université de Nice, Sophia Antipolis, France

  Pascal Chossat

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