A new geometric method and its applications in the three-body problem

In 2000, Chenciner and Montgomery proved the existence of the figure-eight solution in the planar three-body problem with equal masses by using the variational method. Since then, a number of new periodic solutions have been discovered and proven to exist. A workshop on Variational Methods in Celestial Mechanics was organized by Chenciner and Montgomery in 2003 to address the possible applications of variational method in studying the Newtonian N-body problem, while several open problems were proposed by the attending experts. The existence of the Broucke-Henon orbit is one of these open problems, which was proposed by Venturelli. Actually, he noticed that the Schubart orbit with collision is on the closure of the homology class (1, 0, 1). It is not clear if the Broucke-Henon orbit is a minimizer in the homology class (1, 0, 1). By introducing a new geometric argument, we show that under an appropriate topological constraint, the action minimizer must be either the Schubart orbit or the Broucke-Henon orbit. Our geometric argument can be applied to many orbits in the three-body and four-body problem.

举办单位：数学与统计学院

发 布 人：吴双 发布时间： 2018-06-08

发 布 人：吴双 发布时间： 2018-06-08

严夺魁，北京航空航天大学数学与系统科学学院副教授，应用数学系主任，院长助理。主要研究领域是N体问题，指标迭代理论，哈密顿系统等。已经在Journal of Differential Equations, Nonlinearity, Celestial Mechanics & Dynamical Astronomy，Discrete and Continuous Dynamical Systems-Series A等国际上有重要影响的杂志发表文章十余篇。