The high type quadratic Siegel disks are Jordan domains

Mitsuhiro Shishikura, Fei Yang

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…