Sur la structure des ensembles de Fatou p-adiques

2004/12/08 by Juan Rivera-Letelier, Juan Rivera‐Letelier, Rivera-Letelier, Juan · 1 citation
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #advanced mathematical theories #math.DS

paper · pdf · doi:10.48550/arxiv.math/0412180

A preprint of January 2002

arxiv created 2004/12/08 · openalex publication_date 2004/12/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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