Closed geodesics on compact symmetric spaces of higher rank

2022/03/28 by Wu, Weisheng
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.14872

Abstract

In this article, we consider a compact symmetric space M of higher rank. Let P(t) be the set of free-homotopy classes containing a closed geodesic on M with length at most t, and # P(t) its cardinality. We obtain the following asymptotic estimates: #P(t)=\frace^htht(1+O(e^-ut)) for some u>0, where h is the topological entropy of the geodesic flow.

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