Holomorphic Dynamical Systems : Lectures Given at the C.i.m.e. Summer School Held in Cetraro, Italy, July 7-12, 2008

Abate, Marco; Bedford, Eric; Brunella, Marco; Dinh, Tien-Cuong; Schleicher, Dierk

ISBN 10: 3642131700 / ISBN 13: 9783642131707

Published by Springer, 2010

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Bibliographic Details

• Title: Holomorphic Dynamical Systems : Lectures Given at the C.i.m.e. Summer School Held in Cetraro, Italy, July 7-12, 2008
• Publisher: Springer
• Publication Date: 2010
• Language: English
• ISBN 10: 3642131700
• ISBN 13: 9783642131707
• Binding: Soft cover
• Condition: As New

About this title

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.

From the Back Cover

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. This volume collects the Lectures held at the 2008 CIME session on "Holomorphic Dynamical Systems" held in Cetraro, Italy. This CIME Course focused on a number of important topics in the study of discrete and continuous dynamical systems, including both local and global aspects, providing a fascinating introduction to many key problems in current research. The contributions provide an ample description of the phenomena occurring in central themes of holomorphic dynamics such as automorphisms and meromorphic self-maps of projective spaces, of entire maps on complex spaces and holomorphic foliations in surfaces and higher dimensional manifolds, elaborating on the different techniques used and familiarizing readers with the latest findings on current research topics.