Home Mathematics Complex Dynamics and Renormalization (AM-135), Volume 135
book: Complex Dynamics and Renormalization (AM-135), Volume 135
Book
Licensed
Unlicensed Requires Authentication

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

  • Curtis T. McMullen
Language: English
Published/Copyright: 1995
View more publications by Princeton University Press

About this book

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.

Author / Editor information

Curtis T. McMullen is Professor of Mathematics at the University of California, Berkeley.

Reviews

"This book presents a great many ideas very clearly and should prove to be a valuable addition to the complex dynamics literature."

"Curtis T. McMullen, Winner of the 1998 Fields Medal, International Congress of Mathematicians"


Publicly Available Download PDF
i

Publicly Available Download PDF
v

Requires Authentication Unlicensed

Licensed
Download PDF
1

Requires Authentication Unlicensed

Licensed
Download PDF
9

Requires Authentication Unlicensed

Licensed
Download PDF
35

Requires Authentication Unlicensed

Licensed
Download PDF
53

Requires Authentication Unlicensed

Licensed
Download PDF
65

Requires Authentication Unlicensed

Licensed
Download PDF
83

Requires Authentication Unlicensed

Licensed
Download PDF
97

Requires Authentication Unlicensed

Licensed
Download PDF
121

Requires Authentication Unlicensed

Licensed
Download PDF
135

Requires Authentication Unlicensed

Licensed
Download PDF
141

Requires Authentication Unlicensed

Licensed
Download PDF
167

Requires Authentication Unlicensed

Licensed
Download PDF
177

Requires Authentication Unlicensed

Licensed
Download PDF
187

Requires Authentication Unlicensed

Licensed
Download PDF
207

Requires Authentication Unlicensed

Licensed
Download PDF
213

Publishing information
Pages and Images/Illustrations in book
eBook published on:
March 2, 2016
eBook ISBN:
9781400882557
Pages and Images/Illustrations in book
Main content:
214
Other:
31 line drawings
Downloaded on 24.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/9781400882557/html
Scroll to top button