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

• 成果类型: Article
• 署名作者: Knieper, G
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/120995
• 发表日期: 1998
• 页码: 291-314
• 关键词: nonpositively curved manifolds

摘要

In this paper we prove a conjecture of A. Katok, stating; that the geodesic flow on a compact rank 1 manifold admits a uniquely determined invariant 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 set of singular closed geodesics is strictly smaller than the topological entropy.