Semigroup actions on tori and stationary measures on projective spaces

Yves Guivarc'H, Roman Urban

Let $\Gamma$ be a sub-semigroup of $G=GL(d,\mathbb{R}),$ $d>1.$ We assume that the action of $\Gamma$ on ${\mathbb{R}}^d$ is strongly irreducible and that $\Gamma$ contains a proximal and expanding element.…