A short proof of unique ergodicity of horospherical foliations on infinite volume hyperbolic manifolds
Confluentes Mathematici, Tome 8 (2016) no. 1, pp. 165-174.

We provide a new proof of the fact that the horospherical group N<G=SO o (d,1) acting on the frame bundle ΓG 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.

Reçu le : 2015-04-30
Révisé le : 2015-07-06
Accepté le : 2015-09-14
Publié le : 2016-09-28
DOI : https://doi.org/10.5802/cml.29
Classification : 22E40,  22D40,  28D15,  37A17,  37A25
Mots clés: unique ergodicity, horospherical group, frame bundle, in nite volume hyperbolic manifolds
@article{CML_2016__8_1_165_0,
     author = {Barbara Schapira},
     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 = {cml.centre-mersenne.org/item/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. https://cml.centre-mersenne.org/item/CML_2016__8_1_165_0/

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