Description: The Ergodic Theory has its roots in the investigation of time-evolution and chaotic properties of complex physical systems. It was discovered that many such systems exhibit stable behavior on large time scales. The Ergodic Theory seeks for a rigorous explanation of this surprising phenomenon. In mathematical terms this involves analysis of groups of transformations of measure spaces that will be the main focus of the course. For instance, we will be interested in asymptotic behavior of iterations of these transformations, how to characterize randomness in this context, and how to compare/classify such systems. We will also discuss some of the applications of the Ergodic Theory to the other areas of mathematics.
