The action of abelian C^1-diffeomorphisms group fixing a point on C^n
Résumé
In this paper, we study the action of any abelian subgroup G of Diff^{1}(C^n) on C^n. Suppose that 0 in Fix(G) and dim(vect(L_{G}))=n, where vect(L_{G}) is the vector space generated by L_{G}={Df_{0}, f in G }. We prove the existence of 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. Moreover, if G has a dense orbit in C^{n} then every orbit of U_{q} is dense in C^{n}.
Domaines
Systèmes dynamiques [math.DS]
Origine : Fichiers produits par l'(les) auteur(s)