Complex Dynamics and Renormalization (AM-135), Volume 135 / Curtis T. McMullen.

Format:

Book

Author/Creator:

McMullen, Curtis T., author.

Series:

Annals of mathematics studies ; no. 135.

Annals of Mathematics Studies ; 317

Language:

English

Subjects (All):

Renormalization (Physics).

Polynomials.

Dynamics.

Mathematical physics.

Physical Description:

1 online resource (229 pages) : illustrations.

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

In English.

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.

Contents:

Frontmatter

Contents

Chapter 1. Introduction

Chapter 2. Background in conformal geometry

Chapter 3. Dynamics of rational maps

Chapter 4. Holomorphic motions and the Mandelbrot set

Chapter 5. Compactness in holomorphic dynamics

Chapter 6. Polynomials and external rays

Chapter 7. Renormalization

Chapter 8. Puzzles and infinite renormalization

Chapter 9. Robustness

Chapter 10. Limits of renormalization

Chapter 11. Real quadratic polynomials

Appendix A. Orbifolds

Appendix B. A closing lemma for rational maps

Bibliography

Index

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400882557

1400882559

OCLC:

954123972