Dynamical Systems Seminar

Equilibrium states for geodesic flows over compact rank 1 manifolds and sufficiently regular potential functions were studied recently by Burns, Climenhaga, Fisher and myself. We showed that if the higher rank set does not carry full topological pressure then the equilibrium state is unique. In this talk, I will describe new joint work with Ben Call, which shows that these equilibrium states have the Kolmogorov property. When the manifold has dimension at least 3 (for example, the interesting case of the Gromov example of a graph manifold) this is a new result even for the Knieper-Bowen-Margulis measure of maximal entropy.