STABLE MANIFOLDS OF TWO-DIMENSIONAL BIHOLOMORPHISMS ASYMPTOTIC TO FORMAL CURVES
Résumé
Let F ∈ Diff(C 2 , 0) be a germ of a holomorphic diffeomorphism and let Γ be an invariant formal curve of F. Assume that the restricted diffeomorphism F | Γ is either hyperbolic attracting or rationally neutral non-periodic (these are the conditions that the diffeomorphism F | Γ should satisfy, if Γ were convergent, in order to have orbits converging to the origin). Then we prove that F has finitely many stable manifolds, either open domains or parabolic curves, consisting of and containing all converging orbits asymptotic to Γ. Our results generalize to the case where Γ is a formal periodic curve of F .
Origine : Fichiers produits par l'(les) auteur(s)
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