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Dynamics: Introductory Lectures

John Milnor

No publication date has been set. Here is a 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
3.2 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
4.2 Recurrence and wandering
4.3 Transitivity and minimality
4.4 Chaos: sensitive dependence, mixing
4.5 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