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Applied Mathematical Sciences Ser.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by John Guckenheimer and Philip Holmes (1983, Hardcover)

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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.

Informazioni su questo prodotto

Product Identifiers

PublisherSpringer New York

ISBN-100387908196

ISBN-139780387908199

eBay Product ID (ePID)154682

Product Key Features

Number of PagesXvi, 462 Pages

LanguageEnglish

Publication NameNonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

SubjectDifferential Equations / General, Mathematical Analysis

Publication Year1983

FeaturesReprint

TypeTextbook

Subject AreaMathematics

AuthorJohn Guckenheimer, Philip Holmes

SeriesApplied Mathematical Sciences Ser.

FormatHardcover

Dimensions

Item Height0.4 in

Item Weight66.3 Oz

Item Length9.2 in

Item Width6.1 in

Additional Product Features

Edition Number3

Intended AudienceScholarly & Professional

LCCN97-135723

Dewey Edition21

ReviewsJ. 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, 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, J. Guckenheimer and P. HolmesNonlinear 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

Series Volume Number42

Number of Volumes1 vol.

IllustratedYes

Dewey Decimal510 s

Edition DescriptionReprint

Table Of ContentContents: 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.

SynopsisThis book applied the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking the 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 the reader develop an intuitive feel for the properties involved., 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, 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

LC Classification NumberQA299.6-433