Localisation des points fixes communs pour des difféomorphismes commutants du plan

摘要

We prove that if G ? Diff1(?~2) is an abelian subgroup generated by any family of commuting diffeomorphisms of the plane which are C~1-close to the identity in the strong C~1-topology and there exist a point p ∈ ?~2 whose orbit by G is bounded then the elements of G has a commun fixed point in the convex hull of. Here, denote the topological closure of the orbit of p by G.