Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

John Guckenheimer, Philip Holmes

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English

Springer Verlag
01 February 2002

Mathematics & Sciences; Differential calculus & equations; Applied mathematics; Classical mechanics

Series: Applied Mathematical Sciences

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

By: John Guckenheimer, Philip Holmes
Imprint: Springer Verlag
Country of Publication: United States
Edition: 3rd
Volume: v.42
Dimensions: Height: 234mm, Width: 156mm, Spine: 26mm
Weight: 1.880kg
ISBN: 9780387908199
ISBN 10: 0387908196
Series: Applied Mathematical Sciences
Pages: 484
Publication Date: 01 February 2002
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Hardback
Publisher's Status: Active

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

Reviews for Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

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