Description

Book Synopsis
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 book provides a proof of the Real Fatou Conjecture. It includes a self-contained and complete version of the argument.

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

The Real Fatou Conjecture

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    A Paperback / softback by Jacek Graczyk, Grzegorz Swiatek

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      Book details

      Publisher Princeton University Press
      Published 25 October 1998
      ISBN-13 9780691002583
      978-0691002583
      ISBN-10 0691002584
      Also in:
      Complex analysis, complex variables

      Description

      Book Synopsis
      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 book provides a proof of the Real Fatou Conjecture. It includes a self-contained and complete version of the argument.

      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

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