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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields: 42 (Applied Mathematical Sciences) - Softcover
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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
Reseña del editor
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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- VerlagSpringer
- Erscheinungsdatum2013
- ISBN 10 1461270200
- ISBN 13 9781461270201
- EinbandTapa blanda
- SpracheEnglisch
- Anzahl der Seiten484
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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Applied Mathematical Sciences)
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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
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Springer New York, Springer US, 2013
ISBN 10: 1461270200
ISBN 13: 9781461270201
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Artikel-Nr. 9781461270201
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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Applied Mathematical Sciences)
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Paperback. Zustand: Brand New. reprint edition. 478 pages. 9.25x6.10x1.09 inches. In Stock. Artikel-Nr. x-1461270200
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