Regularity action of abelian linear groups on C^n

Adlene Ayadi (1) , Ezzeddine Salhi (1)

1 Systèmes dynamiques et combinatoire:99UR15-15

In this paper, we give a characterization of the action of any abelian subgroup G of GL(n, C) on C^n. We prove that any orbit of G is regular with order m<=2n. Moreover, we give a method to determine this order. In the other hand, we specify the region of all orbits which are isomorphic. If G is finitely generated, this characterization is explicit.

Mots clés: Orbit; regular; dense orbit; minimal; subgroup

Domaines: Systèmes dynamiques [math.DS]

Adlene Ayadi, Ezzeddine Salhi. Regularity action of abelian linear groups on C^n. 2011. ⟨hal-00594909v3⟩