Książka Ergodic Theory Alex Blumenthal

Ergodic Theory

Język: Angielski
Oprawa: Twarda
Dostępność: Na zamówienie
Wysyłamy za 17-27 dni
284.47
Ergodic theory provides a powerful lens for understanding dynamical systems, recasting disordered an...

Informacje o książce

Język
Angielski
Oprawa
Książka - Twarda
Data wydania
2026
strony
172
EAN
9783032088352
ISBN
3032088356
Enbook ID
49653562
Waga
467

Pełny opis

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.

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