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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

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ISBN-10: 0387908196

ISBN-13: 9780387908199

Edition: 3rd 1983 (Reprint)

Authors: F. John, Jerrold E. Marsden, John Guckenheimer, Philip Holmes, Lawrence Sirovich

List price: $129.00
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From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #Book Review - Engineering Societies Library, New York#1 "An attempt to make research tools concerning `strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." #American Mathematical Monthly#2
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Book details

List price: $129.00
Edition: 3rd
Copyright year: 1983
Publisher: Springer
Publication date: 2/8/2002
Binding: Hardcover
Pages: 462
Size: 6.50" wide x 9.75" long x 1.25" tall
Weight: 1.782
Language: English

Introduction: Differential Equations and Dynamical Systems
An Introduction to Chaos: Four Examples
Local Bifurcations
Averaging and Perturbation from a Geometric Viewpoint
Hyperbolic Sets, Symbolic Dynamics, and Strange Attractors
Global Bifurcations
Local Codimension Two Bifurcations of Flows
Suggestions for Further Reading
Postscript Added at Second Printing