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

Front Cover
Springer Science & Business Media, Jul 31, 2010 - Mathematics - 348 pages
0 Reviews
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.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Discrete Holomorphic Local Dynamical Systems
1
Dynamics of Rational Surface Automorphisms
56
Uniformisation of Foliations by Curves
105
Dynamics in Several Complex Variables Endomorphisms of ProjectiveSpaces and Polynomiallike Mappings
165
Dynamics of Entire Functions
295
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information