The high type quadratic Siegel disks are Jordan domains

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 )