Complex Dynamics 复杂动力学
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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.
目录
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
