Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points

Abstract

We prove that for closed surfaces M with Riemannian metrics without conjugate points and genus ≥2 the geodesic flow on the unit tangent bundle T1M has a unique measure of maximal entropy. Furthermore, this measure is fully supported on T1M, is the limiting distribution of closed orbits, and the flow is mixing with respect to this measure. We formulate conditions under which this result extends to higher dimensions.