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Singularity Theory and Equivariant Symplectic Maps

  • Book
  • © 1993

Overview

Authors:
  1. Thomas J. Bridges
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    You can also search for this author in PubMed   Google Scholar

  2. Jacques E. Furter
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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-VI
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  2. Introduction

    • Thomas J. Bridges, Jacques E. Furter
    Pages 1-8

  3. Generic bifurcation of periodic points

    • Thomas J. Bridges, Jacques E. Furter
    Pages 9-31

  4. Singularity theory for equivariant gradient bifurcation problems

    • Thomas J. Bridges, Jacques E. Furter
    Pages 33-62

  5. Classification of Zq-equivariant gradient bifurcation problems

    • Thomas J. Bridges, Jacques E. Furter
    Pages 63-83

  6. Period-3 points of the generalized standard map

    • Thomas J. Bridges, Jacques E. Furter
    Pages 85-88

  7. Classification of Dq-equivariant gradient bifurcation problems

    • Thomas J. Bridges, Jacques E. Furter
    Pages 89-99

  8. Reversibility and degenerate bifurcation of period-q points of multiparameter maps

    • Thomas J. Bridges, Jacques E. Furter
    Pages 101-118

  9. Periodic points of equivariant symplectic maps

    • Thomas J. Bridges, Jacques E. Furter
    Pages 119-147

  10. Collision of multipliers at rational points for symplectic maps

    • Thomas J. Bridges, Jacques E. Furter
    Pages 149-174

  11. Equivariant maps and the collision of multipliers

    • Thomas J. Bridges, Jacques E. Furter
    Pages 175-183

  12. Back Matter

    Pages 185-226
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Singularity Theory and Equivariant Symplectic Maps

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

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0073471

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1993

  • Softcover ISBN: 978-3-540-57296-1Published: 29 November 1993

  • eBook ISBN: 978-3-540-48040-2Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VI, 230

  • Topics: Manifolds and Cell Complexes (incl. Diff.Topology), Analysis

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