Abstract:

In this seminar we focus on the ergodic and entropy theory on dynamical systems. We first review some classical theories which include the Kolmogorov-Sinai entropy, classification theory on the actions of groups of integers and its specification properties. Next we will introduce the recent results of the sofic and Rokhlin entropies that generalize classical entropy to the actions of countable groups and how to use them to classify actions. Finally, we discuss the classification of actions on countable groups.