Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
Author(s)
Bibliographic Information
Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
（Applied mathematical sciences, v. 42）
Springer, 1990, c1983
3rd printing, rev. and corr
- : us
- : gw
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Note
Originally published 1983
Bibliography: p. [437]-454
Includes index
Description and Table of Contents
- Volume
-
: us ISBN 9780387908199
Description
An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their 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 readers develop an intuitive feel for the properties involved.
Table of Contents
Chapter 1: Introduction: Differential Equations and Dynamical Systems * Chapter 2: An Introduction to Chaos: Four Examples * Chapter 3: Local Bifurcations * Chapter 4: Averaging and Perturbation from a Geometric Viewpoint * Chapter 5: Hyperbolic Sets, Symbolic Dynamics, and Strange Attractors * Chapter 6: Global Bifurcations * Chapter 7: Local Codimension Two Bifurcations of Flows * Appendix * Suggestions for Further Reading * Postscript Added at Second Printing * Glossary * References * Index
- Volume
-
: gw ISBN 9783540908197
Description
This volume applies 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. In this fifth printing the authors have corrected further errors, oversights and updates.
Table of 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.
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