Complex dynamics

by Carleson, Lennart

Type Book

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Title Statements

Full title :Complex dynamics / Lennart Carleson, Theodore W. Gamelin.

Summary

"Complex Dynamics discusses the properties of conformal mappings in the complex plane, a subject that is closely connected to the study of fractals and chaos. Indeed the culmination of the book is a detailed study of the famous Mandelbrot set, which describes very general properties of such mappings. The book focuses on the analytic side of this contemporary subject. The text was developed out of a course taught over several semesters; its focus is to help students and instructors to familiarize themselves with complex dynamics. Topics covered include: conformal and quasi-conformal mappings, fixed points and conjugations, basic rational iteration (the Julia set), classification of periodic components, critical points and expanding maps, some applications of conformal mappings (e.g. Hermann rings), the local geometry of the Fatou set, and quadratic polynomials and the Mandelbrot set"--Publisher description.

Edition Statements

Publication Date:©1993.

Publication Statements

Publisher(s):Springer-Verlag
Place of Publication:New York
Language:eng
Publication Date:©1993.

Notes

"Based on lectures of the first author at UCLA over several winter quarters, particularly 1986 and 1990"--Preface.

The Physical Object

Description:ix, 174 pages : : illustrations ; : 24 cm.

Edition Identifiers

ISBN:0387979425, 9780387979427, 3540979425, 9783540979425
oclc:ocm26719640
LC Classification:QA331.7
Dewey Decimal:515/.9

I. Conformal and Quasiconformal Mappings. 1. Some Estimates on Conformal Mappings. 2. The Riemann Mapping. 3. Montel's Theorem. 4. The Hyperbolic Metric. 5. Quasiconformal Mappings. 6. Singular Integral Operators. 7. The Beltrami Equation -- II. Fixed Points and Conjugations. 1. Classification of Fixed Points. 2. Attracting Fixed Points. 3. Repelling Fixed Points. 4. Superattracting Fixed Points. 5. Rationally Neutral Fixed Points. 6. Irrationally Neutral Fixed Points. 7. Homeomorphisms of the Circle -- III. Basic Rational Iteration. 1. The Julia Set. 2. Counting Cycles. 3. Density of Repelling Periodic Points. 4. Polynomials -- IV. Classification of Periodic Components. 1. Sullivan's Theorem. 2. The Classification Theorem. 3. The Wolff-Denjoy Theorem -- V. Critical Points and Expanding Maps. 1. Siegel Disks. 2. Hyperbolicity. 3. Subhyperbolicity. 4. Locally Connected Julia Sets -- VI. Applications of Quasiconformal Mappings. 1. Polynomial-like Mappings. 2. Quasicircles. 3. Herman Rings. 4. Counting Herman Rings. 5. A Quasiconformal Surgical Procedure -- VII. Local Geometry of the Fatou Set. 1. Invariant Spirals. 2. Repelling Arms. 3. John Domains -- VIII. Quadratic Polynomials. 1…

Subjects

31.42 functions of one complex variable Analytic mappings Analytische functies Applications (Mathématiques) dinamikus rendszerek -- matematika Fixed point theory Fonctions d'une variable complexe Functions of complex variables Mappings (Mathematics) Point fixe, Théorème du Théorème du point fixe