The Real Fatou Conjecture. (AM-144), Volume 144

Jacek Graczyk; Grzegorz Swiatek

Published by Princeton University Press 1999

The Real Fatou Conjecture. (AM-144), Volume 144

Jacek Graczyk and Grzegorz Swiatek

Volume 144 in the series Annals of Mathematics Studies

https://doi.org/10.1515/9781400865185

Overview
Contents

About this book

In 1920, Pierre Fatou expressed the conjecture that--except for special cases--all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This conjecture remains the main open problem in the dynamics of iterated maps. For the logistic family x- ax(1-x), it can be interpreted to mean that for a dense set of parameters "a," an attracting periodic orbit exists. The same question appears naturally in science, where the logistic family is used to construct models in physics, ecology, and economics.

In this book, Jacek Graczyk and Grzegorz Swiatek provide a rigorous proof of the Real Fatou Conjecture. In spite of the apparently elementary nature of the problem, its solution requires advanced tools of complex analysis. The authors have written a self-contained and complete version of the argument, accessible to someone with no knowledge of complex dynamics and only basic familiarity with interval maps. The book will thus be useful to specialists in real dynamics as well as to graduate students.

Author / Editor information

Jacek Graczyk is Assistant Professor of Mathematics at Michigan State University. Grzegorz Swiatek is Associate Professor of Mathematics at Pennsylvania State University.

Topics

Frontmatter Publicly Available Download PDF	i
Contents Publicly Available Download PDF	vii
Chapter 1. Review of Concepts Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 2. Quasiconformal Gluing Requires Authentication Unlicensed Licensed Download PDF	25
Chapter 3. Polynomial-Like Property Requires Authentication Unlicensed Licensed Download PDF	45
Chapter 4. Linear Growth of Moduli Requires Authentication Unlicensed Licensed Download PDF	67
Chapter 5. Quasi conformal Techniques Requires Authentication Unlicensed Licensed Download PDF	109
Bibliography Requires Authentication Unlicensed Licensed Download PDF	143
Index Requires Authentication Unlicensed Licensed Download PDF	147