名师讲坛：龙以明院士-Stability of Lagrangian elliptic solutions of the classical three body problem via index theory

[责任编辑]李敏妍　[信息提供]数学系

报告题目：Stability of Lagrangian elliptic solutions of the classical three body problem via index theory

报告人：Prof. Yiming Long

报告时间：2012年12月28日16:00-17:00

报告地点：东川路800号闵行校区数学楼中会议室

报告人简介：

　　龙以明：数学家，中国科学院院士，第三世界科学院院士。主要研究领域为非线性分析与辛几何。现任南开大学陈省身数学研究所教授，博士生导师，长江学者，中国数学会副理事长。曾获第三世界科学院数学奖、国家自然科学二等奖、中国数学会陈省身数学奖、全国五一劳动奖章、香港求是基金会杰出青年学者奖；被授予全国模范教师称号；曾在国际数学家大会上作45分钟特邀报告。

报告摘要：

Lagrange found his famous elliptic equilateral triangle solutions of the classical planar three body problem in 1772. Linear stability of such solutions has been investigated by perturbation methods and numerical methods. But we are not aware of any rigorous analytical method which relates this stability to the mass parameter of the three bodies and eccentricity of the ellipse in their full range. In this lecture, I shall give an introduction on the new rigorous analytical method developed and recent results obtained jointly by Xijun Hu, Shanzhong Sun and myself on this linear stability problem for the full range of the parameters via index theories for symplectic matrix paths. More precisely, we proved the existence of three curves in the parameter rectangle, which separate the full parameter domain precisely according to the linear stability of Lagrangian elliptic solutions.