Title: Thermodynamic formalism for non-compact locally CAT(-1) geodesic flows via Patterson-Sullivan measures
Speaker: Caleb Dilsavor (OSU)
Abstract: On the geodesic flow of a manifold of pinched negative curvature, there is a natural quasi-product construction of 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 potential, the construction was not as clear due to discrepancies arising from non-uniqueness of extensions of geodesic segments. I will describe a joint work with Daniel Thompson showing that 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, and I will discuss what this means for the thermodynamic formalism.