Soient G un groupe de Lie réel, Λ un réseau de G, un sous-groupe semi-simple connexe sans facteur compact et Γ un sous-semigroupe Zariski dense de H. On montre que toute adhérence de Γ-orbite dans le quotient est homogène. Soit μ une probabilité sur H dont le support est compact et engendre un sous-semigroupe Zariski dense de H. On montre que toute probabilité μ-stationnaire μ-ergodique sur X est homogène.
Let G be a real Lie group, Λ be a lattice of G, H be a connected semisimple subgroup of G with no compact factor and Γ be a Zariski dense sub-semigroup of H. We prove that every Γ-orbit closure in the quotient space is homogeneous. Let μ be a probability measure on G whose support is compact and spans Γ. We prove that every μ-stationary μ-ergodic probability measure on X is Γ-invariant and homogeneous.
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@article{CRMATH_2011__349_5-6_341_0,
author = {Benoist, Yves and Quint, Jean-Fran\c{c}ois},
title = {Mesures stationnaires et ferm\'es invariants des espaces homog\`enes {II}},
journal = {Comptes Rendus. Math\'ematique},
pages = {341--345},
publisher = {Elsevier},
volume = {349},
number = {5-6},
year = {2011},
doi = {10.1016/j.crma.2011.01.015},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.01.015/}
}
TY - JOUR AU - Benoist, Yves AU - Quint, Jean-François TI - Mesures stationnaires et fermés invariants des espaces homogènes II JO - Comptes Rendus. Mathématique PY - 2011 SP - 341 EP - 345 VL - 349 IS - 5-6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.01.015/ DO - 10.1016/j.crma.2011.01.015 LA - fr ID - CRMATH_2011__349_5-6_341_0 ER -
%0 Journal Article %A Benoist, Yves %A Quint, Jean-François %T Mesures stationnaires et fermés invariants des espaces homogènes II %J Comptes Rendus. Mathématique %D 2011 %P 341-345 %V 349 %N 5-6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.01.015/ %R 10.1016/j.crma.2011.01.015 %G fr %F CRMATH_2011__349_5-6_341_0
Benoist, Yves; Quint, Jean-François. Mesures stationnaires et fermés invariants des espaces homogènes II. Comptes Rendus. Mathématique, Tome 349 (2011) no. 5-6, pp. 341-345. doi : 10.1016/j.crma.2011.01.015. http://www.numdam.org/articles/10.1016/j.crma.2011.01.015/
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