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.

arXiv commentFixed 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