Lecture notes on ergodic transformations

Abstract

Content of the lectures is the following. Properties of transformations equivalent to ergodicity. Birkhoff's Theorem. Properties equivalent to weak mixing. On typical properties of transformations. Lego to construct transformations. Typical entropy invariants. Poisson suspensions with completely positive P-entropy. Spectral theorem for unitary operators. Compact factors, Kronecker algebra. Progression recurrence for weakly mixing transformations. Double recurrence for ergodic transformations.