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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields / Edition 1
     

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields / Edition 1

by John Guckenheimer, P.J. Holmes
 

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ISBN-10: 0387908196

ISBN-13: 9780387908199

Pub. Date: 08/01/1983

Publisher: Springer New York

An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work,

Overview

An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

Product Details

ISBN-13:
9780387908199
Publisher:
Springer New York
Publication date:
08/01/1983
Series:
Applied Mathematical Sciences Series , #42
Edition description:
1st ed. 1983. Corr. 6th printing 2002
Pages:
484
Product dimensions:
6.14(w) x 9.21(h) x 0.04(d)

Table of Contents

Chapter 1: Introduction: Differential Equations and Dynamical Systems
• Chapter 2: An Introduction to Chaos: Four Examples
• Chapter 3: Local Bifurcations
• Chapter 4: Averaging and Perturbation from a Geometric Viewpoint
• Chapter 5: Hyperbolic Sets, Symbolic Dynamics, and Strange Attractors
• Chapter 6: Global Bifurcations
• Chapter 7: Local Codimension Two Bifurcations of Flows
• Appendix
• Suggestions for Further Reading
• Postscript Added at Second Printing
• Glossary
• References
• Index

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