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Dynamics, Bifurcation and Symmetry

New Trends and New Tools

  • Book
  • © 1994

Overview

Editors:
  1. Pascal Chossat

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

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Part of the book series: Nato Science Series C: (ASIC, volume 437)

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Table of contents (28 chapters)

  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
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Keywords

About this book

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.

Editors and Affiliations

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

    Pascal Chossat

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