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 th...