Applied Mathematical Sciences

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

Authors: Guckenheimer, John, Holmes, Philip

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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

Reviews

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

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Buy this book

eBook $79.99 net
( price for USA )
  • ISBN 978-1-4612-1140-2
  • digitally watermarked, no DRM
  • included format: PDF
  • eBooks can be used on all Reading Devices
Hardcover $129.00 net
( price for USA )
  • ISBN 978-0-387-90819-9
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days
Softcover $109.00 net
( price for USA )
  • ISBN 978-1-4612-7020-1
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days

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Bibliographic Information

Bibliographic Information
Book Title
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
Series Title
Applied Mathematical Sciences
Series Volume
42
Copyright
1983
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-1140-2
DOI
10.1007/978-1-4612-1140-2
Hardcover ISBN
978-0-387-90819-9
Softcover ISBN
978-1-4612-7020-1
Series ISSN
0066-5452
Edition Number
1
Topics