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Rational Iteration : Complex Analytic Dynamical Systems :  Complex Analytic Dynamical Systems - Norbert Steinmetz

Rational Iteration : Complex Analytic Dynamical Systems

Complex Analytic Dynamical Systems

Hardcover Published: 1993
ISBN: 9783110137651
Number Of Pages: 195
For Ages: 22+ years old

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A self-contained exposition of the theory of Fatou and Julia sets and of more recent developments, which may serve as a textbook for a course following a one-year introduction to analytic function theory, and should prove useful for advanced students as well as mathematicians who want to become acqu

Industry Reviews

"The book under review is a self-contained account of the subject, which assumes a good knowledge of complex analysis. It covers a surprising amount of material in a fairly modest space so that the reader may have to work correspondingly hard." Mathematical Reviews

"The didactic value of the book is completed by a list of exercises which accompanies each section and by the figures created by Turbo Pascal programs which serve to illustrate various theorems and phenomena." Zentralblatt fur Mathematik

List of Special Symbols
Preliminariesp. 1
Basic Notationp. 2
Proper Mappingsp. 4
The Riemann-Hurwitz Formulap. 7
The Poincare Metricp. 10
Capacity and Green's Functionp. 14
The Dynamical Dichotomyp. 19
Two Examplesp. 20
Notationp. 24
The Julia Setp. 28
Montel's Criterionp. 30
Repelling Cyclesp. 35
Stable Domainsp. 39
The Denjoy-Wolff Theoremp. 42
The Fatou Setp. 46
Sullivan's Theoremp. 47
The Fatou-Cremer Classificationp. 54
Bottcher Domainsp. 60
Schroder Domainsp. 66
Leau Domains and Leau Flowersp. 72
Indifferent Cyclesp. 78
The Centre Problemp. 82
Rotation Domainsp. 85
The Existence of Rotation Domainsp. 89
Siegel's Theoremp. 90
The Bryuno-Russmann Theoremp. 96
Arnold's Theoremp. 102
The Geometry of the Julia Setp. 114
Critical Pointsp. 115
Symbolic Dynamicsp. 120
Smooth Julia Setsp. 125
Completely Invariant Stable Domainsp. 132
Boundaries of Stable Domainsp. 137
Miscellaneap. 146
Polynomialsp. 147
The Mandelbrot Setp. 157
Lyubich's Invariant Measurep. 163
Stable Julia Setsp. 173
Permutable Rational Functionsp. 177
Bibliographyp. 183
Indexp. 188
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783110137651
ISBN-10: 3110137658
Series: de Gruyter Studies in Mathematics
Audience: General
For Ages: 22+ years old
Format: Hardcover
Language: English
Number Of Pages: 195
Published: 1993
Publisher: De Gruyter
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.27
Weight (kg): 0.46