On the area rate of perturbed Siegel disks

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.