The dynamic of abelian subgroup of Diff^r(K^n), fixing a point, (K=R or C)
Résumé
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 \Omega_{j} =F_{j}\F_{j-1} is an open subset (for the relative topology) of F_{j} in which every orbit is isomorphic to any orbits meeting its closure. Moreover, if G has a dense orbit in K^n then every orbit of \Omega_{q} is dense in K^n.
Domaines
Systèmes dynamiques [math.DS]
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