Skip to main content
  • Book
  • © 1988

Singularities and Groups in Bifurcation Theory

Volume II

Part of the book series: Applied Mathematical Sciences (AMS, volume 69)

Buying options

eBook USD 169.00
Price excludes VAT (USA)
  • ISBN: 978-1-4612-4574-2
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 219.99
Price excludes VAT (USA)
Hardcover Book USD 219.99
Price excludes VAT (USA)

This is a preview of subscription content, access via your institution.

Table of contents (13 chapters)

  1. Front Matter

    Pages i-xvi
  2. Introduction

    • Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 1-22
  3. Group-Theoretic Preliminaries

    • Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 23-66
  4. Symmetry-Breaking in Steady-State Bifurcation

    • Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 67-140
  5. The Planar Bénard Problem

    • Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 141-163
  6. Equivariant Normal Forms

    • Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 164-207
  7. Equivariant Unfolding Theory

    • Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 208-246
  8. The Traction Problem for Mooney—Rivlin Material

    • Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 247-257
  9. Symmetry-Breaking in Hopf Bifurcation

    • Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 258-323
  10. Hopf Bifurcation with O(2) Symmetry

    • Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 324-362
  11. Further Examples of Hopf Bifurcation with Symmetry

    • Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 363-411
  12. Mode Interactions

    • Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 412-445
  13. Mode Interactions with O(2) Symmetry

    • Martin Golubitsky, Ian Stewart, David G. Schaeffer
    Pages 446-484
  14. The Taylor—Couette System

    • William F. Langford
    Pages 485-512
  15. Back Matter

    Pages 513-536

About this book

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

  • Mathematics Department, University of Houston, Houston, USA

    Martin Golubitsky

  • Mathematics Institute, University of Warwick, Coventry, England

    Ian Stewart

  • Mathematics Department, Duke University, Durham, USA

    David G. Schaeffer

Bibliographic Information

  • Book Title: Singularities and Groups in Bifurcation Theory

  • Book Subtitle: Volume II

  • Authors: Martin Golubitsky, Ian Stewart, David G. Schaeffer

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-1-4612-4574-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1988

  • Hardcover ISBN: 978-0-387-96652-6

  • Softcover ISBN: 978-1-4612-8929-6

  • eBook ISBN: 978-1-4612-4574-2

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: XVI, 536

  • Topics: Group Theory and Generalizations

Buying options

eBook USD 169.00
Price excludes VAT (USA)
  • ISBN: 978-1-4612-4574-2
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 219.99
Price excludes VAT (USA)
Hardcover Book USD 219.99
Price excludes VAT (USA)