A first course in dynamics

✍ Scribed by Hasselblatt B., Katok A.

• Publisher: CUP
• Year: 2003
• Tongue: English
• Leaves: 435
• Category: Library

✦ Synopsis

The theory of dynamical systems has given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introductory text covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. The only prerequisite is a basic undergraduate analysis course. The authors use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory.

✦ Table of Contents

Cover......Page 1
Abstract......Page 2
Title......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 10
1 Introduction......Page 12
Part 1. A course in dynamics: from simple to complicated behavior......Page 40
2 Systems with Stable Asymptotic Behavior......Page 42
3 Linear Maps and Linear Differential Equations......Page 84
4 Recurrence and Equidistribution on the Circle......Page 107
5 Recurrence and Equidistribution in Higher Dimension......Page 154
6 Conservative Systems......Page 166
7 Simple Systems with Complicated
Orbit Structure......Page 207
8 Entropy and Chaos......Page 253
Part 2. Panorama of dynamical systems......Page 268
9 Simple Dynamics as a Tool......Page 270
10 Hyperbolic Dynamics......Page 290
11 Quadratic Maps......Page 310
12 Homoclinic Tangles......Page 329
13 Strange Attractors......Page 342
14 Variational Methods, Twist Maps,
and Closed Geodesics......Page 353
15 Dynamics, Number Theory, and Diophantine
Approximation......Page 376
Reading......Page 397
Appendix......Page 400
Hints and Answers......Page 419
Solutions......Page 425
Index......Page 430