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.
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. This geometric argument can be applied to many orbits in the three-body and four-body problems. The report is based on joint works with Wentian Kuang, Tiancheng Ouyang, Zhifu Xie and Rongchang Liu.
严夺魁，北京航空航天大学副教授，应用数学系主任，院长助理。主要研究兴趣是N体问题，指标迭代理论，哈密顿系统等。已在JDE，DCDS-A，Cele. Mech. Dyn. Astr., Adv. nonlinear Stud.等国际期刊上发表20余篇论文。