华罗庚青年数学论坛综合报告：Newhouse phenomenon in the complex Hénon family

中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

华罗庚青年数学论坛

综合报告

报告人： 张智元 博士（Université Sorbonne Paris Nord）

题  目：Newhouse phenomenon in the complex Hénon family

时  间：2023.06.30（星期五），10:15-11:15

地  点：数学院南楼N913

摘  要：In a work in progress with Artur Avila and Mikhail Lyubich, we show that there are maps in the complex Hénon family with a stable homoclinic tangency. Moreover, we show that any analytic unfolding of a quadratic homoclinic tangency of a dissipative saddle periodic point of a holomorphic map in C² possesses a parameter with a stable homoclinic tangency. We will explain a new mechanism for the stable intersections between two dynamical Cantor sets generated by two classes of conformal IFSs on the complex plane.