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Holomorphic Dynamical Systems - Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 7-12, 2008 (Paperback, 2010 ed.)
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Holomorphic Dynamical Systems - Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 7-12, 2008 (Paperback, 2010 ed.)
Series: C.I.M.E. Foundation Subseries, 1998
Expected to ship within 10 - 15 working days
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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.
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