题目：Mating Siegel and parabolic quadratic polynomials
时间：2023年5月19日10：30:00-11:30
地点：数学院203
报告人：杨飞教授，南京大学
邀请人：肖映青
摘要: Let $f_\theta$ be the quadratic polynomial having an indifferent fixed point at the origin. For any bounded type irrational number $\theta$ and any rational number $\nu$, we prove that $f_\theta$ and $f_\nu$ are conformally mateable, and that the mating is unique up to conjugacy by a Mobius map. This gives an affirmative (partial) answer to a question raised by Milnor in 2004. A crucial ingredient in the proof relies on an expansive property when iterating certain rational maps near Siegel disk boundaries. Combining this with the expanding property in repelling petals of parabolic points, we also prove that the Julia sets of a class of Siegel rational maps with parabolic points are locally connected. This is a joint work with Yuming Fu.
杨飞，南京大学数学系教授，国家优秀青年基金获得者 ，研究方向为复动力系统。已主持国家自然科学基金和江苏省自然科学基金面上项目和青年基金各一项，已发表SCI论文近20篇，部分研究成果发表在Math. Ann. Transactions of AMS, IMRN，Ergodic Theory and Dynamical Systems和Math.Zeitschrift等期刊上。
