Bifurcation and Symmetry

Cross Influence between Mathematics and Applications

  • Eugene L. Allgower
  • Klaus Böhmer
  • Martin Golubitsky

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Eugene L. Allgower, Klaus Böhmer, Mei Zhen
    Pages 1-10
  3. D. G. Aronson, S. A. van Gils, M. Krupa
    Pages 11-22
  4. Klaus Böhmer, Mei Zhen
    Pages 49-58
  5. F. H. Busse, R. M. Clever
    Pages 59-73
  6. Gerhard Dangelmayr, Michael Kirby
    Pages 85-97
  7. Michael Dellnitz, Martin Golubitsky, Ian Melbourne
    Pages 99-109
  8. Michael Dellnitz, Jerrold E. Marsden, Ian Melbourne, Jürgen Scheurle
    Pages 111-122
  9. Werner Fischer, Elke Koch
    Pages 123-133
  10. Eckart W. Gekeler
    Pages 147-156
  11. Kurt Georg, Rick Miranda
    Pages 157-168
  12. P. Laure, J. Menck, J. Scheurle
    Pages 191-202
  13. Vladimír Janovský, Petr Plecháč
    Pages 203-213
  14. Alexander I. Khibnik, Roman M. Borisyuk, Dirk Roose
    Pages 215-228
  15. E. Knobloch, M. Silber
    Pages 241-252
  16. Reiner Lauterbach
    Pages 253-262
  17. Hans D. Mittelmann, K.-T. Chang, D. F. Jankowski, G. P. Neitzel
    Pages 275-284
  18. Back Matter
    Pages 328-328

About this book


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

Editors and affiliations

  • Eugene L. Allgower
    • 1
  • Klaus Böhmer
    • 2
  • Martin Golubitsky
    • 3
  1. 1.Dept. of MathematicsColorado State UniversityFort CollinsUSA
  2. 2.Fachbereich MathematikUniversität MarburgMarburgGermany
  3. 3.Dept. of MathematicsUniversity of HoustonHoustonUSA

Bibliographic information