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OverviewErgodic 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 DetailsAuthor: Simon Rubinstein-SalzedoPublisher: American Mathematical Society Imprint: American Mathematical Society ISBN: 9781470479206ISBN 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 ![]() 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 ContentsIntroduction 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 IndexReviewsAuthor InformationSimon Rubinstein-Salzedo, Euler Circle, Mountain View, CA Tab Content 6Author Website:Countries AvailableAll regions |