Abstract
Let X be a globally symmetric space of noncompact type and rank greater that one, 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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Link, G. Growth of conjugacy classes of Schottky groups in higher rank symmetric spaces. manuscripta math. 126, 375–391 (2008). https://doi.org/10.1007/s00229-008-0187-6
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DOI: https://doi.org/10.1007/s00229-008-0187-6