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Normally Hyperbolic Invariant Manifolds in Dynamical Systems

  • Textbook
  • © 1994

Overview

Authors:
  1. Stephen Wiggins

    1. Applied Mechanics Department 104-44, California Institute of Technology, Pasadena, USA

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction, Motivation, and Background

    • Stephen Wiggins
    Pages 1-19

  3. Background from the Theory of Differentiable Manifolds

    • Stephen Wiggins
    Pages 21-49

  4. Persistence of Overflowing Invariant Manifolds— Fenichel’s Theorem

    • Stephen Wiggins
    Pages 51-109

  5. The Unstable Manifold of an Overflowing Invariant Manifold

    • Stephen Wiggins
    Pages 111-130

  6. Foliations of Unstable Manifolds

    • Stephen Wiggins
    Pages 131-157

  7. Miscellaneous Properties and Results

    • Stephen Wiggins
    Pages 159-163

  8. Examples

    • Stephen Wiggins
    Pages 165-183

  9. Back Matter

    Pages 185-194
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Keywords

About this book

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.

Authors and Affiliations

  • Applied Mechanics Department 104-44, California Institute of Technology, Pasadena, USA

    Stephen Wiggins

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