Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields / by John Guckenheimer, Philip Holmes.

Format:

Book

Author/Creator:

Guckenheimer, John, author.

Holmes, Philip, author.

Contributor:

SpringerLink (Online service)

Series:

Applied mathematical sciences (Springer-Verlag New York Inc.) 0066-5452 ; 42.

Applied Mathematical Sciences, 0066-5452 ; 42

Language:

English

Subjects (All):

Mathematical analysis.

Analysis (Mathematics).

Analysis.

Local Subjects:

Analysis.

Physical Description:

1 online resource.

Edition:

First edition 1983.

Contained In:

Springer Nature eBook

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1983.

System Details:

text file PDF

Summary:

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.

Contents:

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.

Other Format:

Printed edition:

ISBN:

9781461211402

Access Restriction:

Restricted for use by site license.