# Rudiments de Dynamique Holomorphe

Share this page
*François Berteloot; Volker Mayer*

A publication of the Société Mathématique de France

This book is an introduction to rational iteration theory. In the first four
chapters, the authors deal with the classical theory. The basic properties of
the Julia set and its complement, the Fatou set, are presented; the highest
points of the treatment are the classification of the components of the Fatou
set and Sullivan's non-wandering theorem.

The second part of the book studies several topics in more detail. The authors
begin by considering at length two classes of rational maps: the chaotic maps
and the hyperbolic maps. In the closing chapters, they include respectively a
study of holomorphic families of rational maps with a view to discussing
Fatou's famous problem concerning the density of hyperbolic maps and an
exposition of the methods of potential theory, touching on questions of
ergodicity, which may serve as a preparation for generalizations in higher
dimensions.

A number of the developments treated here appear for the first time in book
form. Several original proofs are presented.

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 interested in dynamical systems and ergodic theory.