Ergodic Theory and Dynamical Systems

Research Article

Entropy estimates for geodesic flows

P. Sarnaka1

a1 Courant Institute for Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA

Abstract

Let M be a compact Riemannian manifold of (variable) negative curvature. Let h be the topological entropy and hμ the measure entropy for the geodesic flow on the unit tangent bundle to M. Estimates for h and hμ in terms of the ‘geometry’ of M are derived. Connections with and applications to other geometric questions are discussed.

(Received August 22 1981)