Smooth Siegel disks without number theory

Abstract

AbstractX. Buff and A. Chéritat proved that there are quadratic polynomials having Siegel disks with smooth boundaries. Based on a simplification of Avila, we give yet another simplification of their proof. The main tool used is a harmonic function introduced by Yoccoz whose boundary values are the sizes of the Siegel disks. The proof also applies to some other families of polynomials, entire and meromorphic functions.