Author | Carleson, Lennart. author |
---|---|
Title | Complex Dynamics [electronic resource] / by Lennart Carleson, Theodore W. Gamelin |
Imprint | New York, NY : Springer New York, 1993 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4364-9 |
Descript | IX, 192 p. online resource |
I. Conformal and Quasiconformal Mappings -- 1. Some Estimates on Conformal Mappings -- 2. The Riemann Mapping -- 3. Montelโs 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. Sullivanโs 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. The Mandelbrot Set -- 2. The Hyperbolic Components of ? -- 3. Greenโs Function of ?c -- 4. Greenโs Function of ? -- 5. External Rays with Rational Angles -- 6. Misiurewicz Points -- 7. Parabolic Points -- Epilogue -- References -- Symbol Index