报告题目：Global surfaces of section and periodic orbits in the spatial isosceles three body problem
报 告 人：欧昱伟
工作单位：山东大学 数学学院
报告时间：2022-11-18 14:30-15:30
腾讯会议ID：365 707 244
报告摘要：In this talk, we study the spatial isosceles three body problem, which is a system with two degrees of freedom after modulo the rotation symmetry. For certain choices of energy and angular momentum, the energy surface is 3- sphere and we find an open book structure where each page is disk-like global surfaces of section for the Hamiltonian flow with the Euler orbit as their common boundary, and a brake orbit passing through them. By considering the Poincare maps of these global surfaces of section, we prove the existence of all kinds of different symmetric periodic orbits under the nonresonant assumption. Moreover, we are able to prove that the system always has infinitely many symmetric periodic orbits on generic energy surface. We also established formulas between the mean index and rotation numbers. This work is jointed with Xijun Hu, Lei Liu and Guowei Yu.
报告人简介：
欧昱伟，教授，博士生导师，研究领域为微分方程与动力系统，主要研究辛道路的Maslov-型指标理论、哈密顿系统迹公式及其在N体问题中的应用。2015年毕业于山东大学，获理学博士学位，师从胡锡俊教授；2015年-2017年在陈省身数学研究所从事博士后研究，师从龙以明院士。取得的主要成果有推广了哈密顿系统的Krein型迹公式、给出了经典拉格朗日解稳定区域和不稳定区域的定量估计；对椭圆相对平衡解建立碰撞指标，给出欧拉解接近碰撞时稳定性分叉现象的理论解释；将Moeckel关于麦克斯韦土星环的稳定性结果推广到任意离心率情形。相关成果发表在ARMA，CMP，Nonlinearity，JDE等高水平学术期刊中。
