Ergodic Theory

Author:   Simon Rubinstein-Salzedo
Publisher:   American Mathematical Society
ISBN:  

9781470479206


Pages:   228
Publication Date:   30 June 2025
Format:   Paperback
Availability:   Not yet available   Availability explained
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Ergodic Theory


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Overview

Ergodic theory is concerned with the measure-theoretic or statistical properties of a dynamical system. This book provides a conversational introduction to the topic, guiding the reader from the classical questions of measure theory to modern results such as the polynomial recurrence theorem. Applications to number theory and combinatorics enhance the exposition, while also presenting the utility of ergodic theory in other areas of research. The book begins with an introduction to measure theory and the Lebesgue integral. After this, the key concepts of the subject are covered: measure-preserving transformations, ergodicity, and invariant measures. These chapters also cover classical results such as Poincare's recurrence theorem and Birkhoff's ergodic theorem. The book ends with more advanced topics, such as mixing, entropy, and an appendix on the weak* topology. Each chapter ends with numerous exercises with a range of difficulty levels, including a handful of open problems. An excellent resource for anyone wishing to learn about ergodic theory, the book only assumes prior exposure to proof-based mathematics. Familiarity with real analysis would be ideal but is not required.

Full Product Details

Author:   Simon Rubinstein-Salzedo
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
ISBN:  

9781470479206


ISBN 10:   1470479206
Pages:   228
Publication Date:   30 June 2025
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Not yet available   Availability explained
This item is yet to be released. You can pre-order this item and we will dispatch it to you upon its release.

Table of Contents

Introduction to measure theory The Lebesgue integral Some limit theorems Measure-preserving transformations The Poincare recurrence theorem Ergodicity Invariant measures Mixing Multiple recurrence and Szemeredi's theorem Polynomial recurrence Entropy The weak* topology Bibliography Index

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Simon Rubinstein-Salzedo, Euler Circle, Mountain View, CA

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