Finiteness of Bowen-Margulis-Sullivan Measures on Certain Manifolds Without Conjugate Points

Abstract

This article studies the Bowen-Margulis-Sullivan (BMS) measures on non-compact manifolds without conjugate points. The finiteness of this measure on the unit tangent space indicates some important dynamical properties. Under the assumptions of uniform visibility axiom and Axiom 2, we give a criterion when the BMS measure is finite.

Keywords

Manifolds without conjugate points / geodesic flows / Bowen-Margulis-Sullivan measure