Introduction to Ergodic Theory

Course content

Overview Of measure spaces. Measure-preserving transfornations. Recurrence and the Poincaré recurrence theorem. Ergodic transformations. The Birkhoff ergodic theorem and von Neumann mean ergodi? theorem. Applications of ergodic theorems, Weak and strong mixing transformations. Isomorphism and factors of measure-preserving transformations. Basics of topological Dynamics. Existence of invariant measures for continuous transformations and the KryIoff-Bogoliouboff theorem.Various selected advanced topics such ag measure-theoretic entropy etc.