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arXiv · 1608.04106

The high type quadratic Siegel disks are Jordan domains

Mitsuhiro Shishikura·Fei Yang
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Abstract

Let $α$ be an irrational number of sufficiently high type and suppose $P_α(z)=e^{2πiα}z+z^2$ has a Siegel disk $Δ_α$ centered at the origin. We prove that the boundary of $Δ_α$ is a Jordan curve, and that it contains the critical point $-e^{2πiα}/2$ if and only if $α$ is a Herman number.

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Mitsuhiro Shishikura, Fei Yang. 2024-04-20. The high type quadratic Siegel disks are Jordan domains. https://arxiv.org/abs/1608.04106

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