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Arithmetic conditions for Julia sets to have positive area
Jianyong Qiao, Hongyu Qu
In this paper, for quadratic polynomials with Cremer points or Siegel disks whose boundaries don't contain critical points, we give an arithmetic condition for their Julia sets to…
On quadratic Siegel disks with a class of unbounded type rotation numbers
Hongyu Qu, Jianyong Qiao, Guangyuan Zhang
In this paper we explore a class of quadratic polynomials having Siegel disks with unbounded type rotation numbers. We prove that any boundary point of Siegel disks of these polyno…
On the area rate of perturbed Siegel disks
Jianyong Qiao, Hongyu Qu
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…
Obstacles to periodic orbits hidden at fixed point of holomorphic maps
Jianyong Qiao, Hongyu Qu
Let be a germ of an -dimensional holomorphic map. Assume that the origin is an isolated fixed point of each iterate of . Then $\{\…
Area of Julia sets of non-renormalizable cubic polynomials
Jianyong Qiao, Hongyu Qu
The long-standing problem of existence of nowhere dense rational Julia set with positive area has been solved by an example in quadratic polynomials by Buff and Chéritat. Since the…