Transcendental Dynamics and Complex Analysis

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Paperback | 26 June 2008

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472 Pages

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After the pioneering work on complex dynamics by Fatou and Julia in the early 20th century, Noel Baker went on to lay the foundations of transcendental complex dynamics. As one of the leading exponents of transcendental dynamics, he showed how developments in complex analysis such as Nevanlinna theory could be applied. His work has inspired many others to take up this increasingly active subject, and will continue to do so. Presenting papers by researchers in transcendental dynamics and complex analysis, this book is written in honour of Noel Baker. The papers describe the state of the art in this subject, with new results on completely invariant domains, wandering domains, the exponential parameter space, and normal families. The inclusion of comprehensive survey articles on dimensions of Julia sets, buried components of Julia sets, Baker domains, Fatou components of functions of small growth, and ergodic theory of transcendental meromorphic functions means this is essential reading for students and researchers in complex dynamics and complex analysis.

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'Baker's work in transcendental meromorphic functions was both pioneering and legendary and his influence in that and related fields has moved friends, colleagues and former students to produce both survey articles and new results, making this both a satisfying and lively tribute.' SciTech Book News

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Complex Analysis Functional Analysis & Transforms

Introduction
Iteration of inner functions and boundaries of components of the Fatou set
Conformal automorphisms of finitely connected regions
Meromorphic functions with two completely invariant domains
A family of matings between transcendental entire functions and a Fuchsian group
Singular perturbations of z^n
Residual Julia sets of rational and transcendental functions
Bank-Laine functions via quasiconformal surgery
Generalisations of uniformly normal families
Entire functions with bounded Fatou components
On multiply connected wandering domains of entire functions
Fractal measures and ergodic theory of transcendental meromorphic functions
Combinatorics of bifurcations in exponential parameter space
Baker domains
Escaping points of the cosine family
Dimensions of Julia sets of transcendental meromorphic functions
Abel's functional equation and its role in the problem of croissance r_guli+re
Table of Contents provided by Publisher. All Rights Reserved.

Transcendental Dynamics and Complex Analysis

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