Name: Ergodic Theory. A Probabilistic Approach to Dynamical Systems
SKU: 64806123
Price: 2132.00 TWD
Availability: InStock
Author: Alex Blumenthal;Lai-Sang Young
ISBN: 9783032088352

portada Ergodic Theory. A Probabilistic Approach to Dynamical Systems

Ergodic Theory. A Probabilistic Approach to Dynamical Systems

Type

Physical Book

Publisher

Springer Nature Switzerland AG

Author

Alex Blumenthal;Lai-Sang Young

Collection

Texts in Applied Mathematics

Year

2025

Pages

184

Format

Hardcover

Dimensions

23.5x15.5 cm

ISBN13

9783032088352

Ergodic Theory. A Probabilistic Approach to Dynamical Systems

Alex Blumenthal;Lai-Sang Young (Author) · Springer Nature Switzerland AG · Hardcover

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Synopsis "Ergodic Theory. A Probabilistic Approach to Dynamical Systems"

Ergodic theory provides a powerful lens for understanding dynamical systems, recasting disordered and seemingly random behavior in the language of probability theory. This book offers a concise, rigorous introduction to the subject, suitable both as a graduate-level textbook and as a reference for both pure and applied mathematicians. Part I (Chapters 1–7) lays the foundation, covering invariant measures, measure-theoretic isomorphisms, ergodicity, mixing, entropy, and culminating in the Shannon–McMillan–Breiman Theorem. Part II (Chapters 8–13) shifts focus to continuous maps of metric spaces, exploring the collection of invariant measures corresponding to a given map. Part III (Chapters 14–16) presents advanced topics rarely found in textbooks at this level, including SRB measures, their deep connection to entropy and Lyapunov exponents, and extensions to two important settings: random and infinite-dimensional dynamical systems. Throughout, the authors emphasize not only the mathematical elegance of ergodic theory but also its practical relevance and rich connections to other areas of mathematics, from information theory to stochastic processes.