On the area rate of perturbed Siegel disks

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 i...

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Veröffentlicht in:Nonlinearity 2024-12, Vol.37 (12), p.125022
Hauptverfasser: Qiao, Jianyong, Qu, Hongyu
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37F25
37F50
Lebesgue measure of Julia sets
parabolic renormalization
quadratic polynomials
Siegel disks
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description 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.
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subjects 37F25
37F50
Lebesgue measure of Julia sets
parabolic renormalization
quadratic polynomials
Siegel disks
title On the area rate of perturbed Siegel disks
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