Normally Hyperbolic Invariant Manifolds in Dynamical Systems

  • Stephen Wiggins

Part of the Applied Mathematical Sciences book series (AMS, volume 105)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Stephen Wiggins
    Pages 1-19
  3. Stephen Wiggins
    Pages 131-157
  4. Stephen Wiggins
    Pages 159-163
  5. Stephen Wiggins
    Pages 165-183
  6. Back Matter
    Pages 185-194

About this book

Introduction

In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom. An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds. In recent years these techniques have been used for the development of global perturbation methods, the study of resonance phenomena in coupled oscillators, geometric singular perturbation theory, and the study of bursting phenomena in biological oscillators. "Invariant manifold theorems" have become standard tools for applied mathematicians, physicists, engineers, and virtually anyone working on nonlinear problems from a geometric viewpoint. In this book, the author gives a self-contained development of these ideas as well as proofs of the main theorems along the lines of the seminal works of Fenichel. In general, the Fenichel theory is very valuable for many applications, but it is not easy for people to get into from existing literature. This book provides an excellent avenue to that. Wiggins also describes a variety of settings where these techniques can be used in applications.

Keywords

dynamical systems dynamics manifold

Authors and affiliations

  • Stephen Wiggins
    • 1
  1. 1.Applied Mechanics Department 104-44California Institute of TechnologyPasadenaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4312-0
  • Copyright Information Springer-Verlag New York 1994
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8734-6
  • Online ISBN 978-1-4612-4312-0
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • About this book