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数学学科学术报告(严夺魁 北京航空航天大学)

发布者:项晓玲   发布时间:2018-12-20  浏览次数:347

报告题目:A new geometric method and its applications in the N-body problem

 告 人:严夺魁 教授 北京航空航天大学

    间:1226 10:00--11:00

    点:20幢第一会议室

报告摘要: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.