Holomorphic Dynamical Systems: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 7-12, 2008 (C.I.M.E. Foundation Subseries)

✍ Scribed by Nessim Sibony, Dierk Schleicher, Dinh Tien Cuong, Marco Brunella, Eric Bedford, Marco Abate, Graziano Gentili (editor), Giorgio Patrizio (editor), Jacques Guenot (editor)

• Publisher: Springer
• Year: 2010
• Tongue: English
• Leaves: 357
• Category: Library

✦ Synopsis

The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. A holomorphic dynamical system is the datum of a complex variety and a holomorphic object (such as a self-map or a vector ?eld) acting on it. The study of a holomorphic dynamical system consists in describing the asymptotic behavior of the system, associating it with some invariant objects (easy to compute) which describe the dynamics and classify the possible holomorphic dynamical systems supported by a given manifold. The behavior of a holomorphic dynamical system is pretty much related to the geometry of the ambient manifold (for instance, - perbolic manifolds do no admit chaotic behavior, while projective manifolds have a variety of different chaotic pictures). The techniques used to tackle such pr- lems are of variouskinds: complexanalysis, methodsof real analysis, pluripotential theory, algebraic geometry, differential geometry, topology. To cover all the possible points of view of the subject in a unique occasion has become almost impossible, and the CIME session in Cetraro on Holomorphic Dynamical Systems was not an exception.

✦ Table of Contents

Holomorphic Dynamical Systems
Preface
Contents
List of Contributors
Discrete Holomorphic Local Dynamical Systems
Dynamics of Rational Surface Automorphisms
Uniformisation of Foliations by Curves
Dynamics in Several Complex Variables: Endomorphisms of ProjectiveSpaces and Polynomial-like Mappings
Dynamics of Entire Functions