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arXiv · 1508.05854

Ergodic geometry for non-elementary rank one manifolds

Gabriele Link·Jean-Claude Picaud
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Abstract

Let $X$ be a Hadamard manifold, and $Γ$ a non-elementary discrete group of isometries of $X$ which contains a rank one isometry. We relate the ergodic theory of the geodesic flow of the quotient orbifold $M=X/Γ$ to the behavior of the Poincar{é} series of $Γ$. Precisely, the aim of this paper is to extend the so-called theorem of Hopf-Tsuji-Sullivan -- well-known for manifolds of pinched negative curvature -- to the framework of rank one orbifolds. Moreover, we derive some important properties for $Γ$-invariant conformal densities supported on the geometric limit set of $Γ$.

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Gabriele Link, Jean-Claude Picaud. 2016-05-07. Ergodic geometry for non-elementary rank one manifolds. https://arxiv.org/abs/1508.05854

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