Relative equilibria for the three-body problem of S^2

报告专家: Perez-Chavela Ernesto (墨西哥自治大学)


2024年4月09日 上午16:15-17:15

2024年4月11日 上午16:15-17:15

2024年4月16日 上午16:15-17:15

2024年4月18日 上午16:15-17:15

报告地点:四川大学数学学院东302  腾讯会议:406-4001-8337


 Lecture 1: Introduction and general aspects of the problem. 

 We will study the historical aspects and approach to the problem as a generalization of the Euler and Lagrange relative equilibria in the Newtonian three body problem.

 Lecture 2: The positive curved three body problem. 

 The natural extension of the Newtonian three body problem to the sphere, is consider that the particles are moving under the influence of the cotangent potential. Then applying the results seen in Lecture 1, we find new families of Euler and Lagrange relative equilibria. 

 Lecture 3: Continuation and bifurcation of relative equilibria.

 We define different kind of bifurcations for the relative equilibria, and we will show how they appear in the three-body problem on the sphere. 

 Lecture 4: Relative equilibria with mass independent shape.

 Until now, we knew that the equilateral triangle on a rotating meridian can form a relative equilibrium for any masses. In this last lecture we will show that in addition to the equilateral triangle, there is an isosceles triangles on a rotating meridian which also form a relative equilibria for any choice of the masses. They are unique with this characteristic. We finish the course with the approach of some open problems.

专家简介:Perez-Chavela Ernesto院士是墨西哥自治大学数学系的教授,他是世界上很有名的天体力学专家,他上世纪九十年代初曾经跟随美国国家科学院院士D.Sarri做博士后,后来回到墨西哥。他还曾担任过墨西哥UAM大学数学系主任,现为墨西哥自治大学教授,墨西哥科学院院士。他在多体问题的Sarri猜测、中心构型、带有曲率的多体问题以及中心构型及其稳定性等方面做出了很多原创性的工作,多篇论文发表在Transactions of the American Mathematical Society,Archive for Rational Mechanics and Analysis, JDE等国际著名刊物上。