Theory of Dynamical Systems

By: D. J. Luo, L. B. Teng

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Hardcover | 1 December 1992

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272 Pages

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This book deals with the global qualitative behaviour of flows and diffeomorphisms. It presents a systematic study of the fundamental theory and method of dynamical systems, from local behaviour near a critical (fixed) point or periodic orbit to the global, such as global structural stability, bifurcations and chaos. It emphasizes the global non-hyperbolicity and introduces some new results obtained by Chinese mathematicians which may not be widely known.

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"... a clear and easy-to-read introduction to dynamical systems in which one can find many definitions, much information and also some important proofs." Robert Roussarie Mathematical Reviews "The style of the book is brief and compact, and the selected materials are lucid and refined. Each topic is stated clearly from the simple to the profound. This book can serve both as an easy-reading introduction to the study field of dynamical systems for the beginner and as a valuable reference for the specialists. Huang Qiyu Mathematics Abstracts

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You Can Find This Book In

Non-Fiction Science Physics Classical Mathematics Dynamics & Statics Engineering & Technology Mechanical Engineering & Materials Materials Science Mechanics of Solids Dynamics & Vibration Mathematics Calculus & Mathematical Analysis

Differential Calculus & Equations Applied Mathematics Chaos Theory Medicine Medicine in General Booktopia Publisher Services World Scientific Publishing

Preface
List of Frequently Used Symbols
Preparations of Differentiable Manifolds and Differential Topology	p. 1
Topological Manifolds and Differentiable Manifolds	p. 1
Local Properties of Differentiable Maps	p. 17
Tangent Bundles and Tangent Maps	p. 26
Introduction to the Morse Theory	p. 35
Sard's Theorem	p. 45
Transversality Theory	p. 51
Dynamical Systems on Manifolds	p. 64
Vector Fields on Manifolds	p. 64
Critical Points of Vector Fields	p. 72
Topological Degrees and Index of Critical Points	p. 75
Flows and Diffeomorphisms	p. 79
Limit Sets and Non-wandering Sets	p. 83
Minimal Sets	p. 89
Local Properties of Flows and Diffeomorphisms	p. 97
Rectification Theorem	p. 97
Behavior Near Critical Points. Linearization	p. 99
Appendix: Introduction to the KAM Theory	p. 107
Hyperbolic Critical Points and Closed Orbits. Local Stable and Unstable Manifolds	p. 111
The [lambda]-lemma	p. 122
Global Stable and Unstable Manifolds	p. 127
Structural Stability and Bifurcations	p. 132
Structural Stability	p. 132
[Omega]-stability and Related Topics	p. 136
Bifurcations of Planar Systems	p. 141
Bifurcations of Toral Trigonometrical Polynomial Systems	p. 148
Codimensional Bifurcations and Unfoldings	p. 153
Bifurcations of Higher Dimensional Systems	p. 158
Chaotic Behavior	p. 164
Symbolic Dynamics	p. 164
Smale's Horseshoe Map	p. 167
Chaotic Behavior of Interval Maps	p. 173
Transversal Homoclinic Theorem	p. 178
The Melnikov's Method	p. 183
Hyperbolic Toral Automorphism	p. 188
A Counter-example on Higher Dimensional Manifold	p. 195
Generic Properties	p. 200
Genericity of g[subscript 0], g[subscript 1](G[subscript 0], G[subscript 1]) Properties	p. 200
Genericity of g[subscript 12] Property	p. 204
Kypka-Smale Theorem	p. 218
Genericity of G[subscript 123] Property	p. 226
Genericity of g[subscript 4], g[subscript 5] Properties	p. 231
References	p. 237
Index	p. 248
Table of Contents provided by Blackwell. All Rights Reserved.

Theory of Dynamical Systems

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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