Colloquium Mathematics - Dr. P. Kunde

Title: (Anti-)classification results in Dynamical Systems and Ergodic Theory

Abstract:

Historically motivated by problems in statistical mechanics Ergodic Theory examines statistical properties of dynamical systems. In particular, one is interested in the long-term behavior of the system as well as the relationship between its time and space averages. A fundamental theme is the so-called isomorphism problem of classifying transformations up to measure-theoretic isomorphism. While it has been solved only for some special classes of transformations, the general problem turns out to be impossible. In this talk, we give an overview of classification as well as anti-classification results in Ergodic Theory and present some related projects.