Angular momentum and Horn problem
报告题目(Title)：Angular momentum and Horn problem
报告人(Speaker)：Alain CHENCINER （巴黎七大，巴黎天文台）
地点(Place)：后主楼1223室
时间(Time)：2019年5月17日10:30-11:30
邀请人(Inviter)：苏喜锋
报告摘要
The relative equilibria of n bodies in R^3 submited to the Newton attraction are certainly the simplest possible solutions of the equations of motion. They exist only for very special configurations, the so-called ``central" configurations whose determination is a very hard problem as soon as the number of bodies exceeds 3. The motions are periodic and necessarily take place in a fixed plane.
Things become mathematically more interesting if one allows the dimension d of ambient space to be greater than 3: in a higher dimensional space, a relative equilibrium is determined not only by the initial configuration but also by the choice of a hermitian structure on the space where the motion takes place; moreover, if the configuration is ``balanced" but not central, the motion is in general quasi-periodic.
I'll address the following questions: what are the possible frequencies of the angular momentum of relative equilibria of a given central (or balanced) configuration and at which values of these frequencies bifurcations from periodic to quasi-periodic relative equilibria do occur ?These questions are nicely related to the classical Horn problem which consists in understanding the possible spectra of a sum of Hermitian (symmetric) matrices whose spectra are given.
主讲人简介
Alain CHENCINER先生是法国巴黎第七大学特级数学教授，Fellow of AMS (American Mathematical Society)，著名的动力系统与三体问题专家，国际数学家大会邀请报告人。他和法国天文学家Jacques LASKAR院士一起创建巴黎天文台天体力学研究所天文学与动力系统研究小组。在中国作家刘慈欣的长篇小说《三体》的第146页，就提到了CHENCINER教授的研究工作。
