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Topological Methods for Variational Problems with Symmetries

  • Authors
  • Thomas┬áBartsch

Part of the Lecture Notes in Mathematics book series (LNM, volume 1560)

Table of contents

  1. Front Matter
    Pages I-X
  2. Thomas Bartsch
    Pages 1-7
  3. Thomas Bartsch
    Pages 53-71
  4. Thomas Bartsch
    Pages 72-85
  5. Thomas Bartsch
    Pages 86-95
  6. Thomas Bartsch
    Pages 96-112
  7. Thomas Bartsch
    Pages 113-126
  8. Back Matter
    Pages 142-154

About this book

Introduction

Symmetry has a strong impact on the number and shape of solutions to variational problems. This has been observed, for instance, in the search for periodic solutions of Hamiltonian systems or of the nonlinear wave equation; when one is interested in elliptic equations on symmetric domains or in the corresponding semiflows; and when one is looking for "special" solutions of these problems. This book is concerned with Lusternik-Schnirelmann theory and Morse-Conley theory for group invariant functionals. These topological methods are developed in detail with new calculations of the equivariant Lusternik-Schnirelmann category and versions of the Borsuk-Ulam theorem for very general classes of symmetry groups. The Morse-Conley theory is applied to bifurcation problems, in particular to the bifurcation of steady states and hetero-clinic orbits of O(3)-symmetric flows; and to the existence of periodic solutions nearequilibria of symmetric Hamiltonian systems. Some familiarity with the usualminimax theory and basic algebraic topology is assumed.

Keywords

Algebraic topology Dynamical systems bifurcation theory critical point theory equivariant topology minimum variational problems

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0073859
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-57378-4
  • Online ISBN 978-3-540-48099-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site