Smooth Siegel disks without number theory: A remark on a proof by Buff and Cheritat

Details Smooth Siegel disks without number theory: A remark on a proof by Buff and Cheritat Smooth Siegel disks without number theory: A remark on a proof by Buff and Cheritat

2005-10-26

arxiv.org/abs/math/0510578v1

Mathematics

Dynamical Systems

5 pages

Scientific paper

X. Buff and A. Cheritat proved that there are quadratic polynomials having Siegel disks with smooth boundaries. Based on a simplification of A. 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.

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