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The high type quadratic Siegel disks are Jordan domains

编辑:wfy 时间:2019年04月17日 访问次数:628

高等数学研究所学术报告

报告题目: The high type quadratic Siegel disks are Jordan domains

报告人:杨飞博士(南京大学)

时间:2019年4月26日 (星期五)下午1:30-2:30

地点:欧阳楼316教室

摘要:Let $\alpha$ be an irrational number of sufficiently high type and suppose that the quadratic polynomial $P_\alpha(z)=e^{2\pi i\alpha}z+z^2$ 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 $\alpha$ satisfies Herman's condition. The main tool in the proof is near-parabolic renormalization. This is a joint work with Mitsuhiro Shishikura.

联系人:尹永成老师yin@zju.edu.cn )