Local product structure for equilibrium states of geodesic flows and applications

Abstract

Let $S$ be a compact surface of genus $\ge 2$ equipped with a metric that is flat everywhere except at finitely many cone points with angles greater than $2\pi$. We examine the geodesic flow on $S$ and prove local product structure for a wide class of equilibrium states. Using this, we establish the Bernoulli property for these systems. We also establish local product structure for a similar class of equilibrium states for geodesic flows on rank 1, nonpositively curved manifolds.

Fixed an issue with Proposition 3.28 in v1. Added an appendix proving local product structure for a wide class of equilibrium states for geodesic flows on rank 1, nonpositively curved manifolds. 51 pages, 5 figures