Relative Equilibria on the S2 Sphere（2）
报告人：Ernesto Pérez-Chavela 教授
报告人单位：Department of Mathematics, ITAM（墨西哥自治理工大学数学系）
报告时间：2022年06月14日（周二）9:00-10:00
报告地点：线上报告（腾讯会议ID：597-290-673，无密码）
摘要：Last week we talked about the existence of families of periodic and quasiperiodic orbits (also called relative periodic orbits) emanating form a kite conguration in the planar four body problem with three equal masses. We introduce a new coordinate system which measures (in the planar four body problem) how far is an arbitrary conguration from a kite conguration. Using these coordinates, and the Lyapunov center theorem, we get families of periodic and quasiperiodic orbits emanating from a kite conguration.
This time we will talk about the relative equilibria on the S2 sphere. The simplest solutions of the N-body problem are those where the mutual distances among the masses remain constant for all time, that is the motions which behave as a rigid body. For N = 3 on the Euclidean space it is well known that there are exactly ve relative equilibria: three collinear (Euler relative equilibria) and two planar forming anequilateral triangle (Lagrange relative equilibria). In this talk I will show a new geometrical technique to study relative equilibria when the masses are on a sphere in 
, when the masses are moving under the inuence of a general attractive potential. In this case collinear relative equilibria means that the masses are on the same geodesic otherwise we call them Lagrange relative equilibria.
报告人简介：Ernesto Pérez-Chavela 教授是墨西哥国家科学院院士，墨西哥ITAM 数学系教授，国际著名的天体力学专家，早年曾跟美国国家科学院院士 D.Sarri做过博士后。Ernesto Pérez-Chavela教授早年在多体问题的中心构型及D.Sarri猜想方面有很好的工作，在国际著名刊物 Archiv Rational Mech., Trans.AMS, Cel.Mech.等发表多篇论文，近十年他与Diacu, Martinez等教授在弯曲空间中的多体问题理论上取得突破，他们在J. of Nonlinear Science,Transacation of AMS, Physica D, J. of Differential Equations , Nonlinearity等重要刊物发表论文多篇。
邀请人：张世清教授
