On the area rate of perturbed Siegel disks

Abstract: In the famous work by Buff and Ch\'eritat 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 Ch\'eritat 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.