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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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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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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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