主题： Global surfaces of section and periodic orbits inthe spatial isosceles three body problem

时间：2023年6月27号 13:00-14:30

地点：腾讯会议: 455-472-213

主持人：符曦 副教授

报告人简介：

　　欧昱伟，山东大学数学学院教授，博士生导师。研究领域为非线性分析与哈密顿系统，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。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等微分方程杂志。

讲座简介：

　　In this talk, we study the spatial isosceles three body problem,which is a system with two degrees of freedom after modulo the rotationsymmetry. For certain choices of energy and angular momentum, the energysurface is 3- sphere and we find an open book structure where each page isdisk-like global surfaces of section for the Hamiltonian flow with the Eulerorbit as their common boundary, and a brake orbit passing through them. Byconsidering the Poincaré maps of these global surfaces of section, we prove theexistence of all kinds of different symmetric periodic orbits under thenonresonant assumption. Moreover, we are able to prove that the system alwayshas infinitely many symmetric periodic orbits on generic energy surface. Wealso established formulas between the mean index and rotation numbers. Thiswork is jointed with Xijun Hu, Lei Liu，Pedro A.S. Salomão and GuoweiYu.