EVENT DETAILS AND ABSTRACT

Title: Polynomial Entropy of Unipotent Flows
Speaker: Kurt Vinhage
Speaker Info: University of Chicago
Brief Description:
Special Note:
Abstract:

Quasi-unipotent flows on homogeneous spaces can be considered the boundary between elliptic actions and hyperbolic ones. When the homogeneous space has a semisimple factor, generic perturbations yield either systems with no orbit complexity (elliptic flows) or exponential complexity (hyperbolic flows). We establish certain polynomial growth rates for quasi-unipotent flows in both the topological and measure-theoretic categories. We also show a variational principal for such flows, characterize actions with no topological orbit growth and use this to exhibit examples in which the variational principal can fail for non-exponential entropies. Joint work with Adam Kanigowski and Daren Wei.