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Rational iteration : complex analytic dynamical systems

Author: Norbert Steinmetz
Publisher: Berlin ; New York : W. de Gruyter, 1993.
Series: De Gruyter studies in mathematics, 16.
Edition/Format:   Print book : EnglishView all editions and formats
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Norbert Steinmetz
ISBN: 3110137658 9783110137651
OCLC Number: 27642988
Description: vi, 189 pages : illustrations ; 25 cm.
Contents: Ch. 1. Preliminaries. 1. Basic Notation. 2. Proper Mappings. 3. The Riemann-Hurwitz Formula. 4. The Poincare Metric. 5. Capacity and Green's Function --
Ch. 2. The Dynamical Dichotomy. 1. Two Examples. 2. Notation. 3. The Julia Set. 4. Montel's Criterion. 5. Repelling Cycles. 6. Stable Domains. 7. The Denjoy-Wolff Theorem --
Ch. 3. The Fatou Set. 1. Sullivan's Theorem. 2. The Fatou-Cremer Classification. 3. Bottcher Domains. 4. Schroder Domains. 5. Leau Domains and Leau Flowers. 6. Indifferent Cycles. 7. The Centre Problem. 8. Rotation Domains --
Ch. 4. The Existence of Rotation Domains. 1. Siegel's Theorem. 2. The Bryuno-Russmann Theorem. 3. Arnold's Theorem --
Ch. 5. The Geometry of the Julia Set. 1. Critical Points. 2. Symbolic Dynamics. 3. Smooth Julia Sets. 4. Completely Invariant Stable Domains. 5. Boundaries of Stable Domains --
Ch. 6. Miscellanea. 1. Polynomials. 2. The Mandelbrot Set. 3. Lyubich's Invariant Measure. 4. Stable Julia Sets. 5. Permutable Rational Functions.
Series Title: De Gruyter studies in mathematics, 16.
Responsibility: Norbert Steinmetz.
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