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Complex Dynamics and Renormalization (AM-135), Volume 135 : Annals of Mathematics Studies (Paperback) - Curtis T. McMullen

Complex Dynamics and Renormalization (AM-135), Volume 135

Annals of Mathematics Studies (Paperback)

Paperback Published: 19th December 1994
ISBN: 9780691029818
Number Of Pages: 214

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Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an "infinitely renormalizable" quadratic polynomial "f(z) = z2 + c." As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial "f." This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set.

The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps.

Industry Reviews

Curtis T. McMullen, Winner of the 1998 Fields Medal, International Congress of Mathematicians "This book presents a great many ideas very clearly and should prove to be a valuable addition to the complex dynamics literature."--Mathematical Reviews

Background in conformal geometry
Dynamics of rational maps
Holomorphic motions and the Mandelbrot set Compactness in holomorphic dynamics
Polynomials and external rays
Renormalization Puzzles and infinite renormalization
Robustness Limits of renormalization
Real quadratic polynomials
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780691029818
ISBN-10: 0691029814
Series: Annals of Mathematics Studies (Paperback)
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 214
Published: 19th December 1994
Country of Publication: US
Dimensions (cm): 23.42 x 15.55  x 1.55
Weight (kg): 0.27