Sur la structure des ensembles de Fatou p-adiques

Details Sur la structure des ensembles de Fatou p-adiques Sur la structure des ensembles de Fatou p-adiques

2004-12-08

arxiv.org/abs/math/0412180v1

Mathematics

Dynamical Systems

A preprint of January 2002

Scientific paper

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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