Soient G un groupe de Lie réel simple, Λ un réseau de G et Γ un sous-groupe Zariski dense de G. On montre que toute orbite de Γ dans le quotient est finie ou dense. Soit μ une probabilité sur G dont le support est compact et engendre un sous-groupe Zariski dense de G. On montre que toute probabilité μ-stationnaire et μ-ergodique sur X est de support fini ou est G-invariante.
Let G be a real simple Lie group, Λ be a lattice of G and Γ be a Zariski dense subgroup of G. We prove that every Γ-orbit in the quotient is either finite or dense. Let μ be a probability measure on G whose support is compact and generates a Zariski dense subgroup of G. We prove that every μ-ergodic μ-stationary probability measure on X either has finite support or is G-invariant.
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Yves Benoist 1 ; Jean-François Quint 2
@article{CRMATH_2009__347_1-2_9_0,
author = {Yves Benoist and Jean-Fran\c{c}ois Quint},
title = {Mesures stationnaires et ferm\'es invariants des espaces homog\`enes},
journal = {Comptes Rendus. Math\'ematique},
pages = {9--13},
publisher = {Elsevier},
volume = {347},
number = {1-2},
year = {2009},
doi = {10.1016/j.crma.2008.11.001},
language = {fr},
}
Yves Benoist; Jean-François Quint. Mesures stationnaires et fermés invariants des espaces homogènes. Comptes Rendus. Mathématique, Volume 347 (2009) no. 1-2, pp. 9-13. doi : 10.1016/j.crma.2008.11.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.11.001/
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