Singularity Theory and Equivariant Symplectic Maps

  • Authors
  • Thomas J. Bridges
  • Jacques E. Furter

Part of the Lecture Notes in Mathematics book series (LNM, volume 1558)

Table of contents

  1. Front Matter
    Pages I-VI
  2. Thomas J. Bridges, Jacques E. Furter
    Pages 1-8
  3. Thomas J. Bridges, Jacques E. Furter
    Pages 9-31
  4. Thomas J. Bridges, Jacques E. Furter
    Pages 33-62
  5. Thomas J. Bridges, Jacques E. Furter
    Pages 63-83
  6. Thomas J. Bridges, Jacques E. Furter
    Pages 85-88
  7. Thomas J. Bridges, Jacques E. Furter
    Pages 89-99
  8. Thomas J. Bridges, Jacques E. Furter
    Pages 119-147
  9. Thomas J. Bridges, Jacques E. Furter
    Pages 149-174
  10. Thomas J. Bridges, Jacques E. Furter
    Pages 175-183
  11. Back Matter
    Pages 185-226

About this book

Introduction

The monograph is a study of the local bifurcations of multiparameter symplectic maps of arbitrary dimension in the neighborhood of a fixed point.The problem is reduced to a study of critical points of an equivariant gradient bifurcation problem, using the correspondence between orbits ofa symplectic map and critical points of an action functional. New results onsingularity theory for equivariant gradient bifurcation problems are obtained and then used to classify singularities of bifurcating period-q points. Of particular interest is that a general framework for analyzing group-theoretic aspects and singularities of symplectic maps (particularly period-q points) is presented. Topics include: bifurcations when the symplectic map has spatial symmetry and a theory for the collision of multipliers near rational points with and without spatial symmetry. The monograph also includes 11 self-contained appendices each with a basic result on symplectic maps. The monograph will appeal to researchers and graduate students in the areas of symplectic maps, Hamiltonian systems, singularity theory and equivariant bifurcation theory.

Keywords

Area Hamiltonian systems bifurcation classification framework function functional hamiltonian system singularity singularity theory symmetry symplectic maps

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0073471
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-57296-1
  • Online ISBN 978-3-540-48040-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book
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