Ruelle's inequality and the Pesin formula for geodesic flows on manifolds without conjugate points

Abstract

In this paper, we prove the existence of Lyapunov exponents for the geodesic flow on complete Riemannian manifolds without conjugate points whose sectional curvature is bounded below. Under suitable additional curvature assumptions, we establish Ruelle's inequality. Furthermore, assuming the same geometric conditions, we obtain the Pesin entropy formula for $C^1$-H\"older geodesic flows on finite-volume manifolds without conjugate points.