关于举行张鹏飞博士学术报告会的通知

报告题目：Homoclinic intersections of lemon billiards

报 告人：张鹏飞博士（University of Oklahoma）

报告时间：2022年12月22日（星期四）上午10:00---11:00

报告地点：腾讯会议：会议ID：206 726 897，会议密码：202212

邀 请人：马东魁教授

欢迎广大师生前往！

数学学院

2022年12月19日

报告摘要: Let Q(b) be the planar domain as the intersection of two unit disks, where 0<b<2 measures the distance between their centers. The dynamical billiards on Q(b) are called lemon billiards since the shape of the domain Q(b) resembles a lemon. The lemon billiards have been studied by Heller and Tomsovic [Physics Today 46 (1993), 38 – 46], in which they demonstrated a clear connection between the classical mechanics and the quantum mechanics: the eigenstates of the quantum billiards are large only at where the periodic trajectories of the classical billiards go. Numerical results in [Chaos 23 (2013), 043137] suggest that the billiard map on Q(b) has positive (topological) entropy. In this talk I will show that for a range of parameters of the lemon billiards, there exist crossing homoclinic intersections for the lemon billiards. In particular, these lemon billiards have positive topological entropy. This talk is based on joint work with Dr. Jin [arXiv:2203.06477].

报告人介绍：张鹏飞，2011年获中国科技大学理学博士学位，2011-2012在北京大学工作，2012-2014在 UMass Amherst 工作，2014-2015在 University of Houston 工作，2015-2017在 University of Mississippi 工作，2017至今在 University of Oklahoma 工作。研究方向为微分动力系统，主要工作集中在部分双曲系统，动力系统的通有性和弹球理论。