Global Bifurcations and Chaos

Analytical Methods

  • Stephen Wiggins

Part of the Applied Mathematical Sciences book series (AMS, volume 73)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Stephen Wiggins
    Pages 171-333
  3. Back Matter
    Pages 475-495

About this book

Introduction

Global Bifurcations and Chaos: Analytical Methods is unique in the literature of chaos in that it not only defines the concept of chaos in deterministic systems, but it describes the mechanisms which give rise to chaos (i.e., homoclinic and heteroclinic motions) and derives explicit techniques whereby these mechanisms can be detected in specific systems. These techniques can be viewed as generalizations of Melnikov's method to multi-degree of freedom systems subject to slowly varying parameters and quasiperiodic excitations. A unique feature of the book is that each theorem is illustrated with drawings that enable the reader to build visual pictures of global dynamcis of the systems being described. This approach leads to an enhanced intuitive understanding of the theory.

Keywords

bifurcation chaos differential equation diffusion dynamical system dynamical systems Eigenvalue Hamiltonian hamiltonian system integrable system invariant manifold ordinary differential equation solution stability

Authors and affiliations

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

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1042-9
  • Copyright Information Springer-Verlag New York, Inc. 1988
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-1041-2
  • Online ISBN 978-1-4612-1042-9
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • About this book
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