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arXiv · 2608.24316

Arithmetic conditions for Julia sets to have positive area

Jianyong Qiao·Hongyu Qu
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Abstract

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 have positive area. Our proof relies on the Siegel Return Machinery as well as the pseudo-Siegel disk theory developed by Dudko and Lyubich.

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Jianyong Qiao, Hongyu Qu. 2026-08-25. Arithmetic conditions for Julia sets to have positive area. https://arxiv.org/abs/2608.24316

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