Ergodic Theory and Dynamical Systems / by Yves Coudène.

Format:

Book

Author/Creator:

Coudène, Yves, Author.

Series:

Universitext, 0172-5939

Language:

English

Undetermined

Subjects (All):

Dynamics.

Ergodic theory.

Dynamical Systems and Ergodic Theory.

Local Subjects:

Dynamical Systems and Ergodic Theory.

Physical Description:

1 online resource (XIII, 190 p. 49 illus., 1 illus. in color.)

Edition:

1st ed. 2016.

Place of Publication:

London : Springer London : Imprint: Springer, 2016.

Summary:

This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions. Detailed explanations are accompanied by numerous examples, including interval maps, Bernoulli shifts, toral endomorphisms, geodesic flow on negatively curved manifolds, Morse-Smale systems, rational maps on the Riemann sphere and strange attractors. Ergodic Theory and Dynamical Systems will appeal to graduate students as well as researchers looking for an introduction to the subject. While gentle on the beginning student, the book also contains a number of comments for the more advanced reader.

Contents:

Introduction

Part I Ergodic Theory

The Mean Ergodic Theorem

The Pointwise Ergodic Theorem

Mixing

The Hopf Argument

Part II Dynamical Systems

Topological Dynamics

Nonwandering

Conjugation

Linearization

A Strange Attractor

Part III Entropy Theory

Entropy

Entropy and Information Theory

Computing Entropy

Part IV Ergodic Decomposition

Lebesgue Spaces and Isomorphisms

Ergodic Decomposition

Measurable Partitions and -Algebras

Part V Appendices

Weak Convergence

Conditional Expectation

Topology and Measures

References.

Notes:

Includes bibliographical references and index.

ISBN:

1-4471-7287-6