EVENT DETAILS AND ABSTRACT

Title: Thermodynamic formalism for non-compact locally CAT(-1) geodesic flows via Patterson-Sullivan measures
Speaker: Caleb Dilsavor
Speaker Info: The Ohio State University
Brief Description:
Special Note:
Abstract:

On the geodesic flow of a manifold of pinched negative curvature, there is a natural quasi-product construction of unique equilibrium states in terms of Patterson-Sullivan measures, which are measures that are defined geometrically on the visual boundary of the universal cover. For a locally CAT(-1) space with a non-constant Hölder potential, the construction was not as clear due to discrepancies arising from non-uniqueness of extensions of geodesic segments in the universal cover. I will describe a joint work with Daniel Thompson showing that, if the potential is bounded and satisfies the Bowen property, then these discrepancies introduce only uniformly bounded errors in the construction, so that Coornaert’s ideas from the Gromov hyperbolic setting can still be applied to obtain an invariant measure. Under an extra finite dimension assumption, we are then able to show this measure is the unique equilibrium state if it is finite.