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© 2002

The Symmetry Perspective

From Equilibrium to Chaos in Phase Space and Physical Space

Textbook

Part of the Progress in Mathematics book series (PM, volume 200)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Martin Golubitsky, Ian Stewart
    Pages 1-31
  3. Martin Golubitsky, Ian Stewart
    Pages 33-57
  4. Martin Golubitsky, Ian Stewart
    Pages 59-86
  5. Martin Golubitsky, Ian Stewart
    Pages 87-122
  6. Martin Golubitsky, Ian Stewart
    Pages 123-159
  7. Martin Golubitsky, Ian Stewart
    Pages 161-199
  8. Martin Golubitsky, Ian Stewart
    Pages 201-220
  9. Martin Golubitsky, Ian Stewart
    Pages 221-240
  10. Martin Golubitsky, Ian Stewart
    Pages 241-274
  11. Martin Golubitsky, Ian Stewart
    Pages 275-300
  12. Back Matter
    Pages 301-325

About this book

Introduction

Pattern formation in physical systems is one of the major research frontiers of mathematics. A central theme of this book is that many instances of pattern formation can be understood within a single framework: symmetry.

The book applies symmetry methods to increasingly complex kinds of dynamic behavior: equilibria, period-doubling, time-periodic states, homoclinic and heteroclinic orbits, and chaos. Examples are drawn from both ODEs and PDEs. In each case the type of dynamical behavior being studied is motivated through applications, drawn from a wide variety of scientific disciplines ranging from theoretical physics to evolutionary biology. An extensive bibliography is provided.

Keywords

Analysis Chaos Vibration chaos theory model modeling

Authors and affiliations

  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK

Bibliographic information

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Reviews

From the reviews:

"This book was awarded the Ferran Sunyier i Balaguer Prize for 2001, and I am sure that it will be a very useful resource not only for researchers in this area but also for those who want to obtain the benefits of using this approach in applications." --Bulletin of the American Mathematical Society (Review of hardcover edition)

[The] rich collection of examples makes the book … extremely useful for motivation and for spreading the ideas to a large Community. This [review] is far from complete and cannot reflect the authors’ unique way of presenting examples, asking questions, giving answers or forming an intuition.”(MATHEMATICAL REVIEWS)