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MiS Preprint
6/1997

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

Gerhard Knieper

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.

Received:
Mar 21, 1997
Published:
Mar 21, 1997

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inJournal
1998 Repository Open Access
Gerhard Knieper

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

In: Annals of mathematics, 148 (1998) 1, pp. 291-314