Semigroup actions on tori and stationary measures on projective spaces

• Autorzy: Yves Guivarc'h , Roman Urban
• Języki publikacji: EN

Abstrakty

EN

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 $𝕋^{d} = ℝ^{d}/ℤ^{d}$ are finite or dense.

Kategorie tematyczne

• 54H20: Topological dynamics
• 60J05: Discrete-time Markov processes on general state spaces
• 60B11: Probability theory on linear topological spaces
• 37C85: Dynamics of group actions other than 𝐙 and 𝐑 , and foliations \SeeMainly{, and also , }

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 171
• Numer: 1
• Strony: 33-66

Daty

wydano

2005

Twórcy

autor

Yves Guivarc'h

• IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France

autor

Roman Urban

• Institute of Mathematics, Wrocław University, Plac Grunwaldzki 2/4, 50-384 Wrocław, Poland

Identyfikatory

DOI

10.4064/sm171-1-3