hal-00521493, version 2
ACTION OF NON ABELIAN GROUP GENERATED BY AFFINE HOMOTHETIES ON R^n
Résumé : 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.
- 1 :
- Faculté des sciences de Sfax
- Domaine : Mathématiques/Systèmes dynamiques
- Mots-clés : Homothety – orbit – density – minimal – non abelian – action – dynamic
- Versions disponibles : v1 (27-09-2010) v2 (28-09-2010) v3 (30-09-2010) v4 (07-10-2010)
- hal-00521493, version 2
- http://hal.archives-ouvertes.fr/hal-00521493
- oai:hal.archives-ouvertes.fr:hal-00521493
- Contributeur :
- Soumis le : Mardi 28 Septembre 2010, 19:43:26
- Dernière modification le : Mardi 28 Septembre 2010, 20:58:58
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