We provide a new proof of the fact that the horospherical group acting on the frame bundle of a hyperbolic manifold admits a unique invariant ergodic measure (up to multiplicative constants) supported on the set of frames whose orbit under the geodesic flow comes back infinitely often in a compact set. This result is known, but our proof is more direct and much shorter.
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Mots clés : unique ergodicity, horospherical group, frame bundle, in nite volume hyperbolic manifolds
@article{CML_2016__8_1_165_0,
author = {Schapira, Barbara},
title = {A short proof of unique ergodicity of horospherical foliations on infinite volume hyperbolic manifolds},
journal = {Confluentes Mathematici},
pages = {165--174},
publisher = {Institut Camille Jordan},
volume = {8},
number = {1},
year = {2016},
doi = {10.5802/cml.29},
language = {en},
url = {http://www.numdam.org/articles/10.5802/cml.29/}
}
TY - JOUR AU - Schapira, Barbara TI - A short proof of unique ergodicity of horospherical foliations on infinite volume hyperbolic manifolds JO - Confluentes Mathematici PY - 2016 SP - 165 EP - 174 VL - 8 IS - 1 PB - Institut Camille Jordan UR - http://www.numdam.org/articles/10.5802/cml.29/ DO - 10.5802/cml.29 LA - en ID - CML_2016__8_1_165_0 ER -
%0 Journal Article %A Schapira, Barbara %T A short proof of unique ergodicity of horospherical foliations on infinite volume hyperbolic manifolds %J Confluentes Mathematici %D 2016 %P 165-174 %V 8 %N 1 %I Institut Camille Jordan %U http://www.numdam.org/articles/10.5802/cml.29/ %R 10.5802/cml.29 %G en %F CML_2016__8_1_165_0
Schapira, Barbara. A short proof of unique ergodicity of horospherical foliations on infinite volume hyperbolic manifolds. Confluentes Mathematici, Tome 8 (2016) no. 1, pp. 165-174. doi : 10.5802/cml.29. http://www.numdam.org/articles/10.5802/cml.29/
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