Dynamique p-adique (d'apr\`es des expos\'es de Jean-Christophe Yoccoz)

TL;DR

This paper introduces the dynamics of rational functions over p-adic fields, summarizing key results and developments from lectures by Jean-Christophe Yoccoz, highlighting contributions from various researchers in the field.

Contribution

It provides an accessible overview of p-adic dynamics, emphasizing recent developments and consolidating results from multiple researchers in a lecture-based format.

Findings

Summarizes key results in p-adic dynamics

Highlights contributions from multiple researchers

Provides an educational overview of the field

Abstract

This paper is an introduction to the dynamics of rational fractions over a p-adic field. It follows the lectures that Jean-Christophe Yoccoz gave during the \'Etats de la recherche in May 2006, and develops certain points. Most of the results to be explained here are due to Benedetto, B\'ezivin, Hsia, Lubin, Morton, Rivera-Letelier and Silverman. ----- Ce texte est une introduction \`a la dynamique des fractions rationnelles sur un corps $p$-adique. Il reprend le cours que Jean-Christophe Yoccoz avait fait lors des \emph{\'Etats de la recherche} de mai 2006 et en d\'eveloppe certains points. La plupart des r\'esultats pr\'esent\'es sont d\^us \`a Benedetto, B\'ezivin, Hsia, Lubin, Morton, Rivera-Letelier et Silverman.