Bifurcation and Symmetry

1. Front Matter

   Pages I-VIII

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2. Exploiting Equivariance in the Reduced Bifurcation Equations

   • Eugene L. Allgower, Klaus Böhmer, Mei Zhen

   Pages 1-10

3. The homoclinic twist bifurcation point

   • D. G. Aronson, S. A. van Gils, M. Krupa

   Pages 11-22

4. High Corank Steady-State Mode Interactions on a Rectangle

   • Peter Ashwin

   Pages 23-33

5. Numerical Investigation of the Bifurcation from Travelling Waves to Modulated Travelling Waves

   • P. Aston, A. Spence, W. Wu

   Pages 35-47

6. Mode Interactions of an Elliptic System on the Square

   • Klaus Böhmer, Mei Zhen

   Pages 49-58

7. Secondary, Tertiary and Quarternary States of Fluid Flow

   • F. H. Busse, R. M. Clever

   Pages 59-73

8. Hopf-type bifurcations in the presence of linear and nonlinear symmetries

   • G. Cicogna

   Pages 75-83

9. On Diffusively Coupled Oscillators

   • Gerhard Dangelmayr, Michael Kirby

   Pages 85-97

10. Mechanisms of Symmetry Creation

    • Michael Dellnitz, Martin Golubitsky, Ian Melbourne

    Pages 99-109

11. Generic Bifurcations of Pendula

    • Michael Dellnitz, Jerrold E. Marsden, Ian Melbourne, Jürgen Scheurle

    Pages 111-122

12. Symmetry Aspects of 3-Periodic Minimal Surfaces

    • Werner Fischer, Elke Koch

    Pages 123-133

13. Hopf bifurcation at non-semisimple eigenvalues: a singularity theory approach

    • J. E. Furter

    Pages 135-145

14. On Trigonometric Collocation in Hopf Bifurcation

    • Eckart W. Gekeler

    Pages 147-156

15. Exploiting Symmetry in Solving Linear Equations

    • Kurt Georg, Rick Miranda

    Pages 157-168

16. Symmetry and Preservation of Nodal Structure in Elliptic Equations Satisfying Fully Nonlinear Neumann Boundary Condtions

    • Timothy J. Healey, Hansjörg Kielhofer

    Pages 169-177

17. A New Approach for Solving Singular Nonlinear Equations

    • Annegret Hoy

    Pages 179-189

18. Quasiperiodic drift flow in the Couette-Taylor problem

    • P. Laure, J. Menck, J. Scheurle

    Pages 191-202

19. Numerical applications of equivariant reduction techniques

    • Vladimír Janovský, Petr Plecháč

    Pages 203-213

20. Numerical Bifurcation Analysis of a Model of Coupled Neural Oscillators

    • Alexander I. Khibnik, Roman M. Borisyuk, Dirk Roose

    Pages 215-228

Symmetry is a property which occurs throughout nature and it is therefore natural that symmetry should be considered when attempting to model nature. In many cases, these models are also nonlinear and it is the study of nonlinear symmetric models that has been the basis of much recent work. Although systematic studies of nonlinear problems may be traced back at least to the pioneering contributions of Poincare, this remains an area with challenging problems for mathematicians and scientists. Phenomena whose models exhibit both symmetry and nonlinearity lead to problems which are challenging and rich in complexity, beauty and utility. In recent years, the tools provided by group theory and representation theory have proven to be highly effective in treating nonlinear problems involving symmetry. By these means, highly complex situations may be decomposed into a number of simpler ones which are already understood or are at least easier to handle. In the realm of numerical approximations, the systematic exploitation of symmetry via group repre­ sentation theory is even more recent. In the hope of stimulating interaction and acquaintance with results and problems in the various fields of applications, bifurcation theory and numerical analysis, we organized the conference and workshop Bifurcation and Symmetry: Cross Influences between Mathematics and Applications during June 2-7,8-14, 1991 at the Philipps­ University of Marburg, Germany.

• Germany
• Variance
• complexity
• growth
• interaction
• mathematics
• nature
• numerical analysis
• preservation
• stability
• university

• Dept. of Mathematics, Colorado State University, Fort Collins, USA

  Eugene L. Allgower

• Fachbereich Mathematik, Universität Marburg, Marburg, Germany

  Klaus Böhmer

• Dept. of Mathematics, University of Houston, Houston, USA

  Martin Golubitsky

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