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Dynamics: Introductory Lectures

 By John Milnor 

 Publication date not yet set

Tentative table of contents

Part I Discursive Introduction 

Chapter 1 Chaotic Dynamics: Some History

1.1  Celestial mechanics

1.2  Poincaré and sensitive dependence

1.3  The restricted 3-body problem

1.4  The first return map

1.5  Ueda, Lorenz, and Hénon

1.6  Further reading

Chapter 2 The Simplest Chaotic Systems

2.1  Two maps of the interval

2.2  Angle doubling

2.3  Sensitive dependence

2.4  Symbolic dynamics

2.5  The solenoid

2.6  Problems for the reader

Chapter 3 Probabilistic Methods

3.1  Bernoulli and Borel: the law of large numbers

 Natural measures and ergodic measures

3.3  Problems for the reader

Part II Topological Dynamics

Chapter 4 Basic Concepts

4.1  Periodicity and limiting behavior

 Recurrence and wandering

4.3  Transitivity and minimality

4.4  Chaos: sensitive dependence, mixing

 Forward expansive maps

4.6  Problems for the reader

Chapter 5 Attraction and Repulsion

        5.1  Trapped attracting sets

5.2  Attractors

5.3  Chain-attractors

5.4  Repelling sets and repellors

5.5  Problems for the reader