© 1983

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields


Part of the Applied Mathematical Sciences book series (AMS, volume 42)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. John Guckenheimer, Philip Holmes
    Pages 1-65
  3. John Guckenheimer, Philip Holmes
    Pages 66-116
  4. John Guckenheimer, Philip Holmes
    Pages 117-165
  5. John Guckenheimer, Philip Holmes
    Pages 166-226
  6. John Guckenheimer, Philip Holmes
    Pages 227-288
  7. John Guckenheimer, Philip Holmes
    Pages 289-352
  8. John Guckenheimer, Philip Holmes
    Pages 353-420
  9. Back Matter
    Pages 421-462

About this book


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


Bifurcations Chaos (Math.) Dynamische Systeme Fields Nichtlineare Schwingung Oscillations Seltsamer Attraktor Vector Verzweigung (Math.) differential equation linear optimization ordinary differential equation

Authors and affiliations

  1. 1.Department of MathematicsCornell UniversityIthacaUSA
  2. 2.Department of Mechanical and Aerospace Engineering and Program in Applied and Computational MathematicsPrinceton UniversityPrincetonUSA

Bibliographic information

  • Book Title Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
  • Authors John Guckenheimer
    Philip Holmes
  • Series Title Applied Mathematical Sciences
  • DOI
  • Copyright Information Springer Science+Business Media New York 1983
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-90819-9
  • Softcover ISBN 978-1-4612-7020-1
  • eBook ISBN 978-1-4612-1140-2
  • Series ISSN 0066-5452
  • Series E-ISSN 2196-968X
  • Edition Number 1
  • Number of Pages XVI, 462
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
  • Buy this book on publisher's site
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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