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

Gabriele Link
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Abstract

Let $X$ be a globally symmetric space of noncompact type, and $Γ\subset\Isom(X)$ a Schottky group of axial isometries. Then $M:=X/Γ$ 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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Gabriele Link. 2005-12-14. Growth of conjugacy classes of Schottky groups in higher rank symmetric spaces. https://arxiv.org/abs/math/0512333

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