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Dominique Cerveau

Dynamique Et G'Om'trie Complexes English

Etienne Ghys

Jean-Christophe Yoccoz

In this book, several masters of the subject provide very nice surveys of or introductions to the subject. It is the tenth volume in this very popular AMS series. These books feature attractive softcovers and very affordable prices for students. They are English versions of bestselling books published by the Socitete Mathematique de France.

Complex Dynamics and Geometry

Marco Abate

Dierk Schleicher

Dinh Tien Cuong

Marco Brunella

Eric Bedford

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.

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

Holomorphic Dynamical Systems

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