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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Applied...
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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Applied...
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by John Guckenheimer and Philip Holmes
Sales Rank : 385688
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Hardcover: 480 pages
Publisher: Springer February 8, 2002
Language: English
ISBN-10: 0387908196
ISBN-13: 978-0387908199
Product Dimensions:
9.4 x 6.3 x 1.3 inches
Shipping Weight: 2 pounds
Product Review
"The book is rewarding readingIts excellent survey of the mathematical literature makes it a valuable reference." -- JOURNAL OF STATISCIAL PHYSICS
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
Product Description
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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