Th\'eor\`emes d'\'equidistribution pour les syst\`emes dynamiques d'origine arithm\'etique

TL;DR

This survey reviews arithmetic equidistribution theorems in algebraic dynamics, focusing on heights, conjectures, and key theorems like Bilu and Baker's on the projective line, highlighting recent developments in the field.

Contribution

It provides a comprehensive overview of arithmetic equidistribution results and conjectures in algebraic dynamics, emphasizing recent progress and open problems.

Findings

Summarizes key equidistribution theorems in algebraic dynamics.

Highlights conjectures and open problems in the field.

Connects heights and dynamical systems in arithmetic contexts.

Abstract

This survey article is about algebraic dynamics. It is mainly concerned by the arithmetic equidistribution theorems featured by dynamical systems. The contents are: - heights - algebraic dynamics, conjectures - equidistribution theorem on the projective line (after Bilu and Baker). It was written for the sesion 2006 of \'Etats de la recherche, Syst\`emes dynamiques polynomiaux.