Mesures stationnaires et fermés invariants des espaces homogènes

Abstract

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 X = G / Λ 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. To cite this article: Y. Benoist, J.-F. Quint, C. R. Acad. Sci. Paris, Ser. I 347 (2009).