Singularities and Groups in Bifurcation Theory

Volume I

  • Martin Golubitsky
  • David G. Schaeffer
Part of the Applied Mathematical Sciences book series (AMS, volume 51)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Martin Golubitsky, David G. Schaeffer
    Pages 1-50
  3. Martin Golubitsky, David G. Schaeffer
    Pages 51-116
  4. Martin Golubitsky, David G. Schaeffer
    Pages 117-181
  5. Martin Golubitsky, David G. Schaeffer
    Pages 182-212
  6. Martin Golubitsky, David G. Schaeffer
    Pages 213-242
  7. Martin Golubitsky, David G. Schaeffer
    Pages 243-288
  8. Martin Golubitsky, David G. Schaeffer
    Pages 289-336
  9. Martin Golubitsky, David G. Schaeffer
    Pages 337-396
  10. Martin Golubitsky, David G. Schaeffer
    Pages 397-416
  11. Martin Golubitsky, David G. Schaeffer
    Pages 417-453
  12. Back Matter
    Pages 455-466

About this book

Introduction

This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob­ lems and we hope to convert the reader to this view. In this preface we will discuss what we feel are the strengths of the singularity theory approach. This discussion then Ieads naturally into a discussion of the contents of the book and the prerequisites for reading it. Let us emphasize that our principal contribution in this area has been to apply pre-existing techniques from singularity theory, especially unfolding theory and classification theory, to bifurcation problems. Many ofthe ideas in this part of singularity theory were originally proposed by Rene Thom; the subject was then developed rigorously by John Matherand extended by V. I. Arnold. In applying this material to bifurcation problems, we were greatly encouraged by how weil the mathematical ideas of singularity theory meshed with the questions addressed by bifurcation theory. Concerning our title, Singularities and Groups in Bifurcation Theory, it should be mentioned that the present text is the first volume in a two-volume sequence. In this volume our emphasis is on singularity theory, with group theory playing a subordinate role. In Volume II the emphasis will be more balanced. Having made these remarks, Iet us set the context for the discussion of the strengths of the singularity theory approach to bifurcation. As we use the term, bifurcation theory is the study of equations with multiple solutions.

Keywords

Area Bifurcations Group theory Groups Volume

Authors and affiliations

  • Martin Golubitsky
    • 1
  • David G. Schaeffer
    • 2
  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA
  2. 2.Department of MathematicsDuke UniversityDurhamUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-5034-0
  • Copyright Information Springer-Verlag New York 1985
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-9533-4
  • Online ISBN 978-1-4612-5034-0
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • About this book