Rational Iteration: Complex Analytic Dynamical Systems

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Walter de Gruyter, Jan 1, 1993 - Mathematics - 195 pages
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Contents

7 The Centre Problem
78
8 Rotation Domains
82
Chapter 4 The Existence of Rotation Domains
85
1 Siegels Theorem
89
2 The BryunoRüssmann Theorem
90
3 Arnolds Theorem
96
Chapter 5 The Geometry of the Julia Set
102
1 Critical Points
114

2 Notation
20
3 The Julia Set
24
4 Montels Criterion
28
5 Repelling Cycles
30
6 Stable Domains
35
7 The DenjoyWolff Theorem
39
Chapter 3 The Fatou Set
42
1 Sullivans Theorem
46
2 The FatouCremer Classification
47
3 Böttcher Domains
54
4 Schröder Domains
60
5 Leau Domains and Leau Flowers
66
6 Indifferent Cycles
72
2 Symbolic Dynamics
115
3 Smooth Julia Sets
120
4 Completely Invariant Stable Domains
125
5 Boundaries of Stable Domains
132
Chapter 6 Miscellanea
137
1 Polynomials
146
2 The Mandelbrot Set
147
3 Lyubichs Invariant Measure
157
4 Stable Julia Sets
163
5 Permutable Rational Functions
173
Bibliography
177
Index
183
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