Singularities and Groups in Bifurcation Theory

Volume II

  • Martin Golubitsky
  • Ian Stewart
  • David G. Schaeffer
Part of the Applied Mathematical Sciences book series (AMS, volume 69)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 1-22
  3. Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 23-66
  4. Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 67-140
  5. Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 141-163
  6. Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 164-207
  7. Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 208-246
  8. Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 247-257
  9. Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 258-323
  10. Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 324-362
  11. Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 363-411
  12. Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 412-445
  13. Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 446-484
  14. William F. Langford
    Pages 485-512
  15. Back Matter
    Pages 513-536

About this book

Introduction

Bifurcation theory studies how the structure of solutions to equations changes as parameters are varied. The nature of these changes depends both on the number of parameters and on the symmetries of the equations. Volume I discusses how singularity-theoretic techniques aid the understanding of transitions in multiparameter systems. This volume focuses on bifurcation problems with symmetry and shows how group-theoretic techniques aid the understanding of transitions in symmetric systems. Four broad topics are covered: group theory and steady-state bifurcation, equicariant singularity theory, Hopf bifurcation with symmetry, and mode interactions. The opening chapter provides an introduction to these subjects and motivates the study of systems with symmetry. Detailed case studies illustrate how group-theoretic methods can be used to analyze specific problems arising in applications.

Keywords

Group theory Irreducibility Lattice group action invariant theory partial differential equation

Authors and affiliations

  • Martin Golubitsky
    • 1
  • Ian Stewart
    • 2
  • David G. Schaeffer
    • 3
  1. 1.Mathematics DepartmentUniversity of HoustonHoustonUSA
  2. 2.Mathematics InstituteUniversity of WarwickCoventryEngland
  3. 3.Mathematics DepartmentDuke UniversityDurhamUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4574-2
  • Copyright Information Springer-Verlag New York 1988
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8929-6
  • Online ISBN 978-1-4612-4574-2
  • Series Print ISSN 0066-5452
  • About this book