Sur la structure des ensembles de Fatou p-adiques
Juan Rivera-Letelier
Abstract
A classification of the periodic components of the Fatou set of p-adic rational maps. Each such periodic component is either an immediate attracting basin or an open affinoid, where the dynamics is quasi-periodic (the p-adic analogues of Siegel discs and Herman rings.) The main tool is a fixed point theorem for connected subsets of Berkovich's projective line (or p-adic hyperbolic space).
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