Smooth Siegel disks via semicontinuity: a remark on a proof of Buff and Cheritat

TL;DR

This paper offers an alternative proof that quadratic Siegel disks have smooth boundaries, utilizing results from Yoccoz and Risler to modify Buff and Cheritat's original argument.

Contribution

It presents a simplified proof of the smoothness of quadratic Siegel disks boundary using existing results, providing a different perspective from the original Buff and Cheritat proof.

Findings

Quadratic Siegel disks have smooth boundaries.

The proof relies on results by Yoccoz and Risler.

The approach is a modification of Buff and Cheritat's argument.

Abstract

Recently, Xavier Buff and Arnaud Cheritat have provided an elegant proof of the existence of quadratic Siegel disks with smooth boundary. In this short note, we show how results of Yoccoz and Risler can be used to conclude the same result. Our proof is a small modification of the argument given by Buff and Cheritat.