On the area rate of perturbed Siegel disks

2021/11/21 by Qiao, Jianyong, Qu, Hongyu
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.10802

Abstract

In the famous work by Buff and Chéritat constructing quadratic Julia sets with positive area, the control of the shape of perturbed Siegel disks is a key technique. To do it, Buff and Chéritat added a restrictive condition on rotation numbers. In this paper, we show that this restrictive condition can be deleted. As a consequence, more quadratic Julia sets with positive area can be constructed.

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