The action of abelian C^1-diffeomorphisms group fixing a point on C^n

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^{1}(C^n) on C^n fixing 0. Suppose that there is x in C^n, having an orbit which generates C^n and also E'(x)=C^n, where E'(x) is the vector space generated by {Df_{0}x, f in G }. We prove the existence of a G-invariant open set U, dense in C^n, in which every orbit is minimal. Moreover, if G has a dense orbit in C^{n} then every orbit of U_{q} is dense in C^{n}.

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

Domaines: Systèmes dynamiques [math.DS]

Yahya N'Dao, Adlene Ayadi. The action of abelian C^1-diffeomorphisms group fixing a point on C^n. 2013. ⟨hal-00721215v5⟩