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Complex Dynamics and Renormalization

Complex Dynamics and Renormalization - Annals of Mathematics Studies

Hardback (14 Mar 1995)

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Publisher's Synopsis

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.

About the Publisher

Princeton University Press

We seek to publish the innovative works of the greatest minds in academia, from the most respected senior scholar to the extraordinarily promising graduate student, in each of the disciplines in which we publish. The Press consciously acquires a collection of titles--a coherent "list" of books--in each discipline, providing focus, continuity, and a basis for the development of future publications.

Book information

ISBN: 9780691029825
Publisher: Princeton University Press
Imprint: Princeton University Press
Pub date:
DEWEY: 530.1430151
DEWEY edition: 20
Language: English
Number of pages: 214
Weight: 490g
Height: 158mm
Width: 242mm
Spine width: 20mm