The uniqueness of the measure of maximal entropy for geodesic flows on rank 1 manifolds

Gerhard Knieper

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Submission date: 21. Mar. 1997
Pages: 23
published in: Annals of mathematics, 148 (1998) 1, p. 291-314 
Bibtex

Abstract:
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.