Holomorphic Dynamical Systems

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.

This volume collects the lectures held at the 2008 CIME session on "Holomorphic Dynamical Systems" held in Cetraro, Italy, which focused on a number of important topics in the study of discrete and continuous dynamical systems.

This title includes contributions by six well known reserchers in different topics of the ample subject

Discrete Holomorphic Local Dynamical Systems.- Dynamics of Rational Surface Automorphisms.- Uniformisation of Foliations by Curves.- Dynamics in Several Complex Variables: Endomorphisms of Projective Spaces and Polynomial-like Mappings.- Dynamics of Entire Functions.