The uniqueness of the measure of maximal entropy for geodesic flows on rank 1 manifolds
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Submission date: 21. Mar. 1997
published in: Annals of mathematics, 148 (1998) 1, p. 291-314
In this paper we prove a conjecture of A. Katok, stating that on a compact rank 1 manifold there exists a uniquely determined measure of maximal entropy. This generalizes previous work of R. Bowen and G. Margulis. As an application we show that the exponential growth rate of the singular closed geodesics is strictly smaller than the topological entropy.