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Complex Dynamics : Universitext / Universitext: Tracts in Mathematics - Lennart Carleson

Complex Dynamics

Universitext / Universitext: Tracts in Mathematics

Paperback Published: 2nd February 1996
ISBN: 9780387979427
Number Of Pages: 192

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Complex dynamics is today very much a focus of interest. Though several fine expository articles were available, by P. Blanchard and by M. Yu. Lyubich in particular, until recently there was no single source where students could find the material with proofs. For anyone in our position, gathering and organizing the material required a great deal of work going through preprints and papers and in some cases even finding a proof. We hope that the results of our efforts will be of help to others who plan to learn about complex dynamics and perhaps even lecture. Meanwhile books in the field a. re beginning to appear. The Stony Brook course notes of J. Milnor were particularly welcome and useful. Still we hope that our special emphasis on the analytic side will satisfy a need. This book is a revised and expanded version of notes based on lectures of the first author at UCLA over several Vinter Quarters, particularly 1986 and 1990. We owe Chris Bishop a great deal of gratitude for supervising the production of course notes, adding new material, and making computer pictures. We have used his computer pictures, and we will also refer to the attractive color graphics in the popular treatment of H. -O. Peitgen and P. Richter. We have benefited from discussions with a number of colleagues, and from suggestions of students in both our courses.

Preface
Conformal and Quasiconformal Mappingsp. 1
Some Estimates on Conformal Mappingsp. 1
The Riemann Mappingp. 5
Montel's Theoremp. 9
The Hyperbolic Metricp. 11
Quasiconformal Mappingsp. 15
Singular Integral Operatorsp. 17
The Beltrami Equationp. 19
Fixed Points and Conjugationsp. 27
Classification of Fixed Pointsp. 27
Attracting Fixed Pointsp. 31
Repelling Fixed Pointsp. 32
Superattracting Fixed Pointsp. 33
Rationally Neutral Fixed Pointsp. 35
Irrationally Neutral Fixed Pointsp. 41
Homeomorphisms of the Circlep. 47
Basic Rational Iterationp. 53
The Julia Setp. 53
Counting Cyclesp. 58
Density of Repelling Periodic Pointsp. 63
Polynomialsp. 65
Classification of Periodic Componentsp. 69
Sullivan's Theoremp. 69
The Classification Theoremp. 74
The Wolff-Denjoy Theoremp. 79
Critical Points and Expanding Mapsp. 81
Siegel Disksp. 81
Hyperbolicityp. 89
Subhyperbolicityp. 91
Locally Connected Julia Setsp. 93
Applications of Quasiconformal Mappingsp. 99
Polynomial-like Mappingsp. 99
Quasicirclesp. 101
Herman Ringsp. 103
Counting Herman Ringsp. 105
A Quasiconformal Surgical Procedurep. 106
Local Geometry of the Fatou Setp. 109
Invariant Spiralsp. 109
Repelling Armsp. 113
John Domainsp. 117
Quadratic Polynomialsp. 123
The Mandelbrot Setp. 123
The Hyperbolic Components of Mp. 133
Green's Function of Tcp. 136
Green's Function of Mp. 139
External Rays with Rational Anglesp. 142
Misiurewicz Pointsp. 148
Parabolic Pointsp. 153
Epiloguep. 161
Referencesp. 163
Indexp. 171
Symbol Indexp. 175
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387979427
ISBN-10: 0387979425
Series: Universitext / Universitext: Tracts in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 192
Published: 2nd February 1996
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.47 x 15.62  x 1.32
Weight (kg): 0.33