报告题目：Rational maps with smooth degenerate Herman rings

报 告 人：杨飞

报告时间：2023年4月13日上午14：15-15：15

报告地点：腾讯会议ID: 310 252 684

摘    要：We prove the existence of rational maps having smooth degenerate Herman rings. This answers a question of Eremenko affirmatively. The proof is based on the construction of smooth Siegel disks by Avila, Buff and Chéritat as well as the classical Siegel-to-Herman quasiconformal surgery. A crucial ingredient in the proof is the surgery's continuity, which relies on the control of the loss of the area of quadratic filled-in Julia sets by Buff and Chéritat. As a by-product, we prove the existence of rational maps having a nowhere dense Julia set of positive area for which these maps have no irrationally indifferent periodic points, no Herman rings, and are not renormalizable.

报告人简介：杨飞，南京大学数学系副教授，研究方向为复动力系统。2013年6月于复旦大学数学科学学院获得博士学位，2013年7月至今在南京大学数学系工作。在 Math. Ann., Trans. AMS, IMRN, Math. Z., Nonlinearity, Ergod. Th. Dynam. Sys., Sci. China Math. 等杂志上发表SCI论文20余篇。已主持国家自然科学基金和江苏省自然科学基金各2项，2022年获国家自然科学基金委优秀青年基金资助。