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  • © 1993

Topological Methods for Variational Problems with Symmetries

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-X
  2. Introduction

    • Thomas Bartsch
    Pages 1-7
  3. The length of G-spaces

    • Thomas Bartsch
    Pages 53-71
  4. The length of representation spheres

    • Thomas Bartsch
    Pages 72-85
  5. The length and Conley index theory

    • Thomas Bartsch
    Pages 86-95
  6. The exit-length

    • Thomas Bartsch
    Pages 96-112
  7. Bifurcation for O(3)-equivariant problems

    • Thomas Bartsch
    Pages 113-126
  8. Back Matter

    Pages 142-154

About this book

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

  • Book Title: Topological Methods for Variational Problems with Symmetries

  • Authors: Thomas Bartsch

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0073859

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1993

  • Softcover ISBN: 978-3-540-57378-4Published: 29 November 1993

  • eBook ISBN: 978-3-540-48099-0Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 158

  • Topics: Algebraic Topology, Analysis, Manifolds and Cell Complexes

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions