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Complex dynamics

Author: Lennart Carleson; Theodore Williams Gamelin
Publisher: New York ; Berlin ; Heidelberg [etc] : Springer, cop. 1993.
Series: Universitext (Berlin. Print)
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

This book discusses the properties of conformal mappings in the complex plane, a subject closely connected to the study of fractals and chaos. Focusing on analytic aspects of this contemporary topic,  Read more...

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Document Type: Book
All Authors / Contributors: Lennart Carleson; Theodore Williams Gamelin
ISBN: 0387979425 9780387979427 3540979425 9783540979425
OCLC Number: 489625842
Description: 1 vol. (IX-174 p.) : ill. ; 24 cm.
Contents: 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. The Mandelbrot Set.- 2. The Hyperbolic Components of ?.- 3. Green's Function of ?c.- 4. Green's Function of ?.- 5. External Rays with Rational Angles.- 6. Misiurewicz Points.- 7. Parabolic Points.- Epilogue.- References.- Symbol Index.
Series Title: Universitext (Berlin. Print)
Responsibility: Lennart Carleson, Theodore W. Gamelin.

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