Texts in Applied Mathematics Ergodic Theory: A Probabilistic Approach to Dynamical Systems, Book 84, (Hardcover)

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. <p></p> <ul> <strong>Part I</strong> (Chapters 1-7) lays the foundation, covering invariant measures, measure-theoretic isomorphisms, ergodicity, mixing, entropy, and culminating in the Shannon-McMillan-Breiman Theorem. <strong>Part II</strong> (Chapters 8-13) shifts focus to continuous maps of metric spaces, exploring the collection of invariant measures corresponding to a given map. <strong>Part III</strong> (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. </ul> <p>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.</p>

• Texts in Applied Mathematics Ergodic Theory: A Probabilistic Approach to Dynamical Systems, Book 84, (Hardcover)
• Author: Alex Blumenthal
• ISBN: 9783032088352
• Format: Hardcover
• Publication Date: 2026-05-19
• Page Count: 209