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Quelques Aspects des Systèmes Dynamiques Polynomiaux
S. Cantat and A. Chambert-Loir, Université de Rennes I, France, and V. Guedj, Université Aix-Marseille 1, France
A publication of the Société Mathématique de France.
cover
Panoramas et Synthèses
2010; 341 pp; softcover
Number: 30
ISBN-10: 2-85629-338-7
ISBN-13: 978-2-85629-338-6
List Price: US$60
Member Price: US$48
Order Code: PASY/30
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This book is concerned with the dynamics of rational transformations of projective varieties and meromorphic transformations of compact Kähler manifolds. Four main viewpoints are developed.

The first article describes the geometry of the varieties which admit a rational transformation with interesting dynamical properties; the geometry constrains the existence of such dynamical systems, but interesting examples with rich dynamics are described.

The second article explains how complex analysis, potential theory, and Hodge theory can be married with methods from dynamical systems to describe the stochastic properties of meromorphic transformations of Kähler manifolds. Then, arithmetic aspects of algebraic dynamical systems are described in a third article; in particular, equidistribution theorems in diophantine geometry and dynamical systems are analyzed and compared.

The fourth article describes the basics of \(p\)-adic dynamics in one variable.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians.

Table of Contents

  • S. Cantat -- Introduction
  • S. Cantat -- Quelques aspects des systèmes dynamiques polynomiaux (Existence, exemples, rigidité)
  • V. Guedj -- Propriétés ergodiques des applications rationnelles
  • A. Chambert-Loir -- Théorèmes d'équidistribution pour les systèmes dynamiques d'origine arithmétique
  • S. Cantat and A. Chambert-Loir -- Dynamique \(p\)-adique (d'après les exposés de Jean-Christophe Yoccoz)
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