Growth of conjugacy classes of Schottky groups in higher rank symmetric spaces

Details Growth of conjugacy classes of Schottky groups in higher rank symmetric spaces Growth of conjugacy classes of Schottky groups in higher rank symmetric spaces

2005-12-14

arxiv.org/abs/math/0512333v1

Mathematics

Differential Geometry

15 pages

Scientific paper

Let $X$ be a globally symmetric space of noncompact type, and $\Gamma\subset\Isom(X)$ a Schottky group of axial isometries. Then $M:=X/\Gamma$ is a locally symmetric Riemannian manifold of infinite volume. The goal of this note is to give an asymptotic estimate for the number of primitive closed geodesics in $M$ modulo free homotopy with period less than $t$.

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