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Itérées d’une famille analytique d’applications holomorphes et points fixes sur un produit

Larbi Belkhchicha, Jean-Pierre Vigué (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper, we consider an analytic family of holomorphic mappings f : M × X X and the sequence f n of iterates of f . If the sequence is not compactly divergent, there exists an unique retraction ρ ( m , . ) adherent to the sequence f n ( m , . ) . If X is a strictly convex taut domain in C n and if the image Λ ( ρ ( m , . ) ) of ρ ( m , . ) is of dimension 1 , we prove that Λ ( ρ ( m , . ) ) does not depend from m M . We apply this result to the existence of fixed points of holomorphic mappings on the product of two bounded strictly convex domains.

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