On the area rate of perturbed Siegel disks

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 is not necessary. As a consequence, more quadratic Julia sets with positive area can be constructed.