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

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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.

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Editorial Reviews

From the Publisher
J. Guckenheimer and P. Holmes

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

"The book is rewarding reading . . . The elementary chapters are suitable for an introductory graduate course for mathematicians and physicists . . . Its excellent survey of the mathematical literature makes it a valuable reference."—JOURNAL OF STATISTICAL PHYSICS

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Product Details

  • ISBN-13: 9780387908199
  • Publisher: Springer New York
  • Publication date: 8/1/1983
  • Series: Applied Mathematical Sciences Series, #42
  • Edition description: 1st ed. 1983. Corr. 6th printing 2002
  • Edition number: 1
  • Pages: 484
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.13 (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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