Cours

Dynamics of holomorphic mapsTien-Cuong Dinh and Nessim SibonyMarch 01, 2007Introductory Lectures (Master)available at http://www.math.jussieu.fr/dinh23PrefaceThis text is written for the students in the Master program at the Universityof Paris 6. Only a knowledge in complex analysis in one variable and in mea-sure theory is required. We begin with the theory of iteration of holomorphicpolynomials and of rational fractions, but our aim is to introduce the readersto the current research in complex dynamics of several variables. We introducethe main dynamical objects and their properties in a way so that they can beeasily extended to the case of higher dimension after introducing the necessarytools in complex analysis of several variables. Since the number of lectures issmall, exercices are given; they contain important results which are used in thetext. This rst version may contain mistakes. Your remarks and comments arewelcome.4Contents1 Fatou-Julia theory for rational fractions 71.1 Dynamics of polynomials . . . . . . . . . . . . . . . . . . . . . . . 71.1.1 Critical and periodic points of polynomials . . . . . . . . . 71.1.2 Dynamics near a xed point . . . . . . . . . . . . . . . . . 101.1.3 Fatou and Julia sets for polynomials . . . . . . . . . . . . 161.1.4 Periodic and wandering Fatou components . . . . . . . . . 171.1.5 Topological entropy and invariant measures . . . . . . . . 211.2 Dynamics of rational fractions . . . . . . . . . . . . ...