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 reno...

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Bibliographic Details

Main Author:	McMullen, Curtis T. 1958- (Author)
Format:	Electronic eBook
Language:	English
Published:	Princeton, NJ Princeton University Press [1995]
Series:	Annals of Mathematics Studies number 135
Subjects:	Mathematische Physik Dynamics Mathematical physics Polynomials Renormalization (Physics) Renormierung Dynamisches System Polynom Dynamik
Online Access:	Volltext
Summary:	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
Item Description:	Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016)
Physical Description:	1 online resource
ISBN:	9781400882557
DOI:	10.1515/9781400882557