Transcendental Dynamics And Complex Analysis
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Transcendental Dynamics and Complex Analysis
Author: Philip J. Rippon
language: en
Publisher: Cambridge University Press
Release Date: 2008-06-26
In honour of Noel Baker, a leading exponent of transcendental complex dynamics, this book describes the state of the art in this subject.
Holomorphic Dynamical Systems
Author: Nessim Sibony
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-07-31
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.
Explorations in Complex Analysis
Author: Michael A. Brilleslyper
language: en
Publisher: American Mathematical Soc.
Release Date: 2012-12-31
Research topics in the book include complex dynamics, minimal surfaces, fluid flows, harmonic, conformal, and polygonal mappings, and discrete complex analysis via circle packing. The nature of this book is different from many mathematics texts: the focus is on student-driven and technology-enhanced investigation. Interlaced in the reading for each chapter are examples, exercises, explorations, and projects, nearly all linked explicitly with computer applets for visualization and hands-on manipulation.