Complex Dynamics 复杂动力学

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　　分類: 图书,进口原版书,科学与技术 Science & Techology ,

作者： Lennart Carleson等著

出版社：

出版时间： 1996-9-1字数：版次： 1页数： 174印刷时间： 1996/09/01开本： 16开印次： 1纸张：胶版纸I S B N ： 9780387979427包装：平装内容简介

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.

Preface

I. Conformal and Quasiconformal Mappings

Some Estimates on Conformal Mappings

The Riemann Mapping

Montel's Theorem

The Hyperbolic Metric

Quasiconformal Mappings

Singular Integral Operators

The Beltrami Equation

II. Fixed Points and Conjugations

Classification of Fixed Points

Attracting Fixed Points

Repelling Fixed Points

Superattracting Fixed Points

Rationally Neutral Fixed Points

Irrationally Neutral Fixed Points

Homeomorphisms of the Circle

III. Basic Rational Iteration

The Julia Set

Counting Cycles

Density of Repelling Periodic Points

Polynomials

IV. Classification of Periodic Components

Sullivan's Theorem

The Classification Theorem

The Wolff-Denjoy Theorem

V. Critical Points and Expanding Maps

Siegel Disks

Hyperbolicity

Subhyperbolicity

Locally Connected Julia Sets

VI. Applications of Quasiconformal Mappings

Polynomial-like Mappings

Quasicircles

Herman Rings

Counting Herman Rings

A Quasiconformal Surgical Procedure

VII. Local Geometry of the Fatou Set

Invariant Spirals

Repelling Arms

John Domains

VIII. Quadratic Polynomials

The Mandelbrot Set

The Hyperbolic Components of M

Green's Function of Jc

Green's Function of M

External Rays with Rational Angles

Misiurewicz Points

Parabolic Points

Epilogue

References

Index

Symbol Index