The dynamic of abelian subgroup of Diff^r(K^n), fixing a point, (K=R or C)

Yahya N'Dao (1) , Adlene Ayadi (1)

1 Systèmes dynamiques et combinatoire:99UR15-15

In this paper, we study the action of any abelian subgroup G of Diff^{r}(K^n), r\geq 1 on K^n, K=R or C. We prove that there exist a decreasing finite sequence F_{0}, F_{1},..., F_{q} of invariant closed sets such that U_{j} =F_{j}\F_{j-1} is an open subset (for the relative topology) of F_{j} in which every orbit is minimal in it.

Mots clés: Diffeomorphisms; abelian; group; orbit; action

Domaines: Systèmes dynamiques [math.DS]

Yahya N'Dao, Adlene Ayadi. The dynamic of abelian subgroup of Diff^r(K^n), fixing a point, (K=R or C). 2012. ⟨hal-00721215v1⟩