Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
Published on 21. November 2013
XVI, 462 pages
978-1-4612-1140-2 (ISBN)
Description
This 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.
Reviews / Votes
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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Other editions
Additional editions
John Guckenheimer | Philip Holmes
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
Book
11/2013
Springer
€181.89
Shipment within 15-20 days
John Guckenheimer | Philip Holmes
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
Book
08/1983
Springer
€181.89
Shipment within 5-7 days
Content
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.
