# Semigroup actions on tori and stationary measures on projective spaces

Studia Mathematica (2005)

- Volume: 171, Issue: 1, page 33-66
- ISSN: 0039-3223

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topYves Guivarc'h, and Roman Urban. "Semigroup actions on tori and stationary measures on projective spaces." Studia Mathematica 171.1 (2005): 33-66. <http://eudml.org/doc/286295>.

@article{YvesGuivarch2005,

abstract = {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.},

author = {Yves Guivarc'h, Roman Urban},

journal = {Studia Mathematica},

keywords = {asymptotic set; proximal and quasi-expanding element; toral automorphism; ID-property; random walk; projective space; stationary measure},

language = {eng},

number = {1},

pages = {33-66},

title = {Semigroup actions on tori and stationary measures on projective spaces},

url = {http://eudml.org/doc/286295},

volume = {171},

year = {2005},

}

TY - JOUR

AU - Yves Guivarc'h

AU - Roman Urban

TI - Semigroup actions on tori and stationary measures on projective spaces

JO - Studia Mathematica

PY - 2005

VL - 171

IS - 1

SP - 33

EP - 66

AB - 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.

LA - eng

KW - asymptotic set; proximal and quasi-expanding element; toral automorphism; ID-property; random walk; projective space; stationary measure

UR - http://eudml.org/doc/286295

ER -

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