Rational Iteration: Complex Analytic Dynamical Systems

Rational Iteration: Complex Analytic Dynamical Systems

by Norbert Steinmetz
     
 

Product Details

ISBN-13:
9783110137651
Publisher:
De Gruyter
Publication date:
04/01/1993
Series:
de Gruyter Studies in Mathematics Series, #16
Pages:
202
Product dimensions:
6.14(w) x 9.21(h) x 0.50(d)
Age Range:
18 Years

Table of Contents

Preface
List of Special Symbols
Ch. 1Preliminaries1
1Basic Notation2
2Proper Mappings4
3The Riemann-Hurwitz Formula7
4The Poincare Metric10
5Capacity and Green's Function14
Ch. 2The Dynamical Dichotomy19
1Two Examples20
2Notation24
3The Julia Set28
4Montel's Criterion30
5Repelling Cycles35
6Stable Domains39
7The Denjoy-Wolff Theorem42
Ch. 3The Fatou Set46
1Sullivan's Theorem47
2The Fatou-Cremer Classification54
3Bottcher Domains60
4Schroder Domains66
5Leau Domains and Leau Flowers72
6Indifferent Cycles78
7The Centre Problem82
8Rotation Domains85
Ch. 4The Existence of Rotation Domains89
1Siegel's Theorem90
2The Bryuno-Russmann Theorem96
3Arnold's Theorem102
Ch. 5The Geometry of the Julia Set114
1Critical Points115
2Symbolic Dynamics120
3Smooth Julia Sets125
4Completely Invariant Stable Domains132
5Boundaries of Stable Domains137
Ch. 6Miscellanea146
1Polynomials147
2The Mandelbrot Set157
3Lyubich's Invariant Measure163
4Stable Julia Sets173
5Permutable Rational Functions177
Bibliography183
Index188

Read More

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >