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

Lukas Geyer
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Abstract

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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Lukas Geyer. 2005-10-26. Smooth Siegel disks without number theory: A remark on a proof by Buff and Cheritat. https://arxiv.org/abs/math/0510578

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