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| HAL : hal-00003343, version 1 |
| arXiv : math.DS/0411553 |
| Fiche détaillée |  Récupérer au format |
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| Studia Mathematica 171, 1 (2005) 33-66 |
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| Semigroup actions on tori and stationary measures on projective spaces |
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| Yves Guivarc'h 1Roman Urban 2 |
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| (2005) |
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| Let $\Gamma$ be a sub-semigroup of $G=GL(d,\mathbb R),$ $d>1.$ We assume that the action of $\Gamma$ on $\R^d$ is strongly irreducible and that $\Gamma$ contains a proximal and expanding element. We describe contraction properties of the dynamics of $\Gamma$ on $\R^d$ at infinity. This amounts to the consideration of the action of $\Gamma$ on some compact homogeneous spaces of $G,$ which are extensions of the projective space $\pr^{d-1}.$ In the case where $\Gamma$ is a sub-semigroup of $GL(d,\R)\cap M(d,\Z)$ and $\Gamma$ has the above properties, we deduce that the $\Gamma$-orbits on $\T^d=\R^d\slash\Z^d$ are finite or dense. |
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| 1 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 2 : | Institut of Mathematics, Wroclaw University |
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Wroclaw university |
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| Domaine | : | Mathématiques/Systèmes dynamiques Mathématiques/Théorie des groupes |
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| limit set – proximal and expanding element – toral automorphism – random walk – projective space – stationary measure |
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| hal-00003343, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00003343 | |
| oai:hal.archives-ouvertes.fr:hal-00003343 | |
| Contributeur : Marie-Annick Guillemer | |
| Soumis le : Mercredi 24 Novembre 2004, 17:27:55 | |
| Dernière modification le : Vendredi 5 Novembre 2010, 11:46:11 | |
