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| HAL: hal-00521493, version 1 |
| arXiv: 1009.5356 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2010-09-27) | v2 (2010-09-28) | v3 (2010-09-30) | v4 (2010-10-07) |
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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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| (2010-09-27) |
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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. (i) Closure of every orbit is an affine subspace of R^n, or union of countable affine subspaces of R^n. (ii) Closure of every orbit is union of at most two closed subgroup of Rn. Furthermore, we show that there exists a G-invariant affine subspace E_G of R^n considered as minimal set of G and every orbit of its complementary U = R^n\E_G is minimal in U. |
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| 1: | Systèmes dynamiques et combinatoire:99UR15-15 |
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Faculté des sciences de Sfax |
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| Subject | : | Mathematics/Dynamical Systems |
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| Homothety – orbit – density – minimal – non abelian – action – dynamic |
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| hal-00521493, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00521493 | |
| oai:hal.archives-ouvertes.fr:hal-00521493 | |
| From: Adlene Ayadi | |
| Submitted on: Monday, 27 September 2010 16:25:52 | |
| Updated on: Monday, 27 September 2010 21:03:45 | |
