Ergodic Theory
A Probabilistic Approach to Dynamical Systems
Buch in deiner Nähe kaufen
Beschreibung
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.
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.
Starts from the basics and emphasizes material in ergodic theory most relevant to a wide audience Explains coverage of extensions of classical theory to random and infinite-dimensional dynamical systems Provides treatment of physical/observable invariant measures, a vital concept in applications
Autor*in
Alex Blumenthal
Themen in »Ergodic Theory«
ergodic theory dynamical systems ergodic theorems mixing properties entropy topological dynamics Lyapunov exponents physical measures SRB measures chaotic dynamical systems smooth ergodic theory statistical properties of dynamical systems random dynamical systems infinite dimensional dynamical systems