EVENT DETAILS AND ABSTRACT

Title: Entropy and Orbit Equivalence in Ergodic Theory
Speaker: Professor Daniel Rudolph
Speaker Info: Colorado Sate University
Brief Description:
Special Note:
Abstract:

I will first offer an overview of two core areas in the dynamics of probability measure preserving dynamical systems, the Kolmogorov-Sinai theory of entropy and the Dye theory of orbit equivalence. Entropy is a nontrivial invariant that, said simply, measures the exponential growth rate of the number of orbits in a dynamical system, a very rough measure of the complexity of the orbit structure. On the other hand, the core theorem of the orbit theory of these systems, due to Henry Dye, says that any two free and ergodic systems are orbit equivalent, that is to say can be regarded as sitting on the same set of orbits. Starting from the seeming conflict between these two notions we will build a revision of Dye's result that precisely accounts for entropy.