The real fatou conjecture

Author(s)

• Graczyk, Jacek
• Świa̦tek, Grzegorz

Bibliographic Information

The real fatou conjecture

by Jacek Graczyk and Grzegorz Świa̦tek

（Annals of mathematics studies, no. 144）

Princeton University Press, 1998

• : cloth
• : pbk

Note

Includes bibliographical references (p. 143-146) and index

Description and Table of Contents

Volume

: cloth ISBN 9780691002576

Description

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 rematins the main open problem in the dynamics of iterated maps. This volume provides 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.

Volume

: pbk ISBN 9780691002583

Description

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.

Table of Contents

1Review of Concepts31.1Theory of Quadratic Polynomials31.2Dense Hyperbolicity61.3Steps of the Proof of Dense Hyperbolicity122Quasiconformal Gluing252.1Extendibility and Distortion262.2Saturated Maps302.3Gluing of Saturated Maps353Polynomial-Like Property453.1Domains in the Complex Plane453.2Cutting Times474Linear Growth of Moduli674.1Box Maps and Separation Symbols674.2Conformal Roughness874.3Growth of the Separation Index1005Quasiconformal Techniques1095.1Initial Inducing1095.2Quasiconformal Pull-back1205.3Gluing Quasiconformal Maps1295.4Regularity of Saturated Maps1335.5Straightening Theorem139Bibliography143Index147

by "Nielsen BookData"

Details

• NCID: BA39122156
• ISBN:
  • 0691002576
  • 0691002584
• LCCN: 98024386
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Princeton, N.J.
• Pages/Volumes: viii, 148 p.
• Size: 24 cm
• Classification:
  • LCC : QA614.58
  • DC21 : 516.3/62
  • NDC8 : 414.7
• Subject Headings:
  • LCSH : Geodesics (Mathematics)
  • LCSH : Polynomials
  • LCSH : Mappings (Mathematics)
• Parent Bibliography ID:
  • BA00300336