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

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

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.

关于扰动Siegel盘的面积率

On the area rate of perturbed Siegel disks

本文研究了扰动Siegel盘的面积率，证明了在构造具有正面积的二次Julia集时，Buff和Chéritat对旋转数添加的限制性条件可以被删除，从而能够构造出更多此类Julia集。

由具有 Siegel 盘的 Lavaurs 映射产生的游荡域

Wandering domains arising from Lavaurs maps with Siegel disks

本文构造了由带 Siegel 型不动点的 Lavaurs 映射产生的新型高维游荡域，并通过抛物曲线与精确收敛速率估计证明捕获域存在的充要条件。