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| HAL : hal-00521493, version 4 |
| arXiv : 1009.5356 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (27-09-2010) | v2 (28-09-2010) | v3 (30-09-2010) | v4 (07-10-2010) |
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| ACTION OF NON ABELIAN GROUP GENERATED BY AFFINE HOMOTHETIES ON R^n |
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| Adlene Ayadi 1Yahya N'Dao 1 |
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| (27/09/2010) |
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| In this paper, we study the action of non abelian group G generated by affine homotheties on R^n. We prove that G satisfies one of the following properties: (i) there exist a subgroup F_{G} of R\{0} containing 0 in its closure, a G-invariant affine subspace E_{G} of R^n and a in E_{G} such that for every x in R^n the closure of the orbit G(x) is equal to F_{G} .(x - a) +E_{G}. In particular, G(x) is dense in E_{G} for every x in E_{G} and every orbit of U = R^n\E_{G} is minimal in U. (ii) there exists a closed subgroup H_{G} of R^n and a in R^n such that for every x in R^n, the closure of the orbit G(x) is equal to the union of (x + H_{G}) and (-x + a + H_{G}). |
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| 1 : | Systèmes dynamiques et combinatoire:99UR15-15 |
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Faculté des sciences de Sfax |
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| Domaine | : | Mathématiques/Systèmes dynamiques |
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| Homothety – orbit – density – minimal – non abelian – action – dynamic |
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| hal-00521493, version 4 | |
| http://hal.archives-ouvertes.fr/hal-00521493 | |
| oai:hal.archives-ouvertes.fr:hal-00521493 | |
| Contributeur : Adlene Ayadi | |
| Soumis le : Mercredi 6 Octobre 2010, 21:33:02 | |
| Dernière modification le : Jeudi 7 Octobre 2010, 08:46:15 | |
