报告题目： A generalized family of transcendental functions with one dimensional Julia sets

报 告 人：  张旭教授， 山东大学（威海），主要关注系统演化规律，研究方向是微分方程和动力系统。

报告日期： 2021-01-27 星期三

报告时间： 8:30-9:30

报告地点： 腾讯会议 ID：733 258 097， 密码:  24680

报告摘要： In this talk, some basic materials on fractal geometry and dynamical systems will be introduced. Further, we talk about the construction of a generalized family of transcendental (non-polynomial entire) functions, where the Hausdorff dimension and the packing dimension of the Julia sets are equal to one, there exist multiply connected wandering domains, the dynamics can be completed described, and for any non-negative number s, there is a function taken from this family with the order of growth s. Baker proved that the Hausdorff dimension of the transcendental function is no less than one in 1975, the minimum value was obtained via an elegant construction by Bishop in 2018. The order of growth is zero in Bishop's construction, the family of functions here have arbitrarily positive or even infinite order of growth.