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- Title
Localisation des points fixes communs pour des difféomorphismes commutants du plan.
- Authors
Firmo, Saponga
- Abstract
We prove that if G ⊂ Diff1(ℝ) is an abelian subgroup generated by any family of commuting diffeomorphisms of the plane which are C-close to the identity in the strong C-topology and there exist a point p ∈ ℝ whose orbit by G is bounded then the elements of G has a commun fixed point in the convex hull of $$\overline {\mathcal{O}_p (G)}$$. Here, $$\overline {\mathcal{O}_p (G)}$$ denote the topological closure of the orbit of p by G.
- Subjects
ABELIAN semigroups; DIFFEOMORPHISMS; PLANE geometry; TOPOLOGY; ORBIT method; ABELIAN groups; MATHEMATICAL proofs
- Publication
Bulletin of the Brazilian Mathematical Society, 2011, Vol 42, Issue 3, p373
- ISSN
1678-7544
- Publication type
Article
- DOI
10.1007/s00574-011-0021-8