Semigroup actions on tori and stationary measures on projective spaces

Yves Guivarc'h ; Roman Urban

Studia Mathematica, Tome 166 (2005), p. 33-66 / Harvested from The Polish Digital Mathematics Library

Résumé

Let Γ be a subsemigroup of G = GL(d,ℝ), d > 1. We assume that the action of Γ on $ℝ^{d}$ is strongly irreducible and that Γ contains a proximal and quasi-expanding element. We describe contraction properties of the dynamics of Γ on $ℝ^{d}$ at infinity. This amounts to the consideration of the action of Γ on some compact homogeneous spaces of G, which are extensions of the projective space $ℙ^{d-1}$. In the case where Γ is a subsemigroup of GL(d,ℝ) ∩ M(d,ℤ) and Γ has the above properties, we deduce that the Γ-orbits on $^{d} = ℝ^{d}/ℤ^{d}$ are finite or dense.

Détail

Publié le : 2005-01-01

Zbl 1087.37022

EUDML-ID : urn:eudml:doc:286295