Description
Book SynopsisIn 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 Contents1Review 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
