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arXiv · 1505.05648

A short proof of unique ergodicity of horospherical foliations on infinite volume hyperbolic manifolds

Barbara Schapira
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Abstract

We give a short proof of the unique ergodicity of the strong stable foliation of the geodesic flow on the frame bundle of a hyperbolic manifold admitting a finite measure of maximal entropy. Equivalently, let G = S0o(n, 1), $Γ$ \textless{} G be a discrete subgroup of G, and G = N AK the Iwasawa decomposition of G. If the geodesic flow on $Γ$\G admits a finite measure of maximal entropy, we prove that the action of N on $Γ$\G by right multiplication admits a unique invariant measure supported on points whose A-orbit does not diverge.

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Barbara Schapira. 2015-05-21. A short proof of unique ergodicity of horospherical foliations on infinite volume hyperbolic manifolds. https://arxiv.org/abs/1505.05648

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