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

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Mitsuhiro Shishikura, Fei Yang. 2016-08-14. The high type quadratic Siegel disks are Jordan domains. https://arxiv.org/abs/1608.04106

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