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 = {Yves Benoist and Jean-Fran\c{c}ois Quint},
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},
}
Yves Benoist; Jean-François Quint. Mesures stationnaires et fermés invariants des espaces homogènes II. Comptes Rendus. Mathématique, Volume 349 (2011) no. 5-6, pp. 341-345. doi : 10.1016/j.crma.2011.01.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.01.015/
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