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Global Bifurcation of Periodic Solutions with Symmetry

  • Authors
  • Bernold Fiedler

Part of the Lecture Notes in Mathematics book series (LNM, volume 1309)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Bernold Fiedler
    Pages 1-14
  3. Bernold Fiedler
    Pages 15-26
  4. Bernold Fiedler
    Pages 27-34
  5. Bernold Fiedler
    Pages 35-47
  6. Bernold Fiedler
    Pages 48-67
  7. Bernold Fiedler
    Pages 68-83
  8. Bernold Fiedler
    Pages 84-91
  9. Bernold Fiedler
    Pages 92-105
  10. Bernold Fiedler
    Pages 106-115
  11. Bernold Fiedler
    Pages 116-134
  12. Back Matter
    Pages 135-144

About this book

Introduction

This largely self-contained research monograph addresses the following type of questions. Suppose one encounters a continuous time dynamical system with some built-in symmetry. Should one expect periodic motions which somehow reflect this symmetry? And how would periodicity harmonize with symmetry? Probing into these questions leads from dynamics to topology, algebra, singularity theory, and to many applications. Within a global approach, the emphasis is on periodic motions far from equilibrium. Mathematical methods include bifurcation theory, transversality theory, and generic approximations. A new homotopy invariant is designed to study the global interdependence of symmetric periodic motions. Besides mathematical techniques, the book contains 5 largely nontechnical chapters. The first three outline the main questions, results and methods. A detailed discussion pursues theoretical consequences and open problems. Results are illustrated by a variety of applications including coupled oscillators and rotating waves: these links to such disciplines as theoretical biology, chemistry, fluid dynamics, physics and their engineering counterparts make the book directly accessible to a wider audience.

Keywords

Mathematica bifurcation dynamical systems singularity system topology

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0082943
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-19234-3
  • Online ISBN 978-3-540-39150-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site