数学科学学院学术报告[2026]104号

（高水平大学建设系列报告1363号）

报告题目：Marchal-type lemmas for the restricted (N+1)-body problem and their applications

报告人：余国巍 研究员（南开大学）

报告时间：2026年11月09日16:30 - 17:30

报告地点：汇文楼1420会议室

报告摘要：Since the proof of the Figure-Eight solution by Chenciner and Montgomery, the direct methods of calculus of variations have had a great success in the classical Newtonian N-body problem. First in periodic solutions and more recently in parabolic, hyperbolic and hyperbolic-parabolic solutions. The foundation of many of these results is Marchal's lemma, which guarantee's fixed-end local minimizers are collision-free and hence classical solutions of the problem.

Meanwhile almost no result is available in the restricted problem through the direct methods of calculus of variations. Mainly due to the lack of a Marchal-type lemma.  In this talk,  we will first explain how to obtain  such lemmas for the restricted problem, then how they can be used to study periodic, hyperbolic and parabolic solutions. This is a joint work with Kuo-chang Chen.

报告人简介：余国巍，南开大学陈省身数学研究所研究员。2013年在美国明尼苏达大学获得基础数学博士学位，2013-2018年分别在加拿大多伦多大学、法国巴黎九大/巴黎天文台、意大利都灵大学、美国国家数学科学研究所（MSRI）从事博士后研究，方向为动力系统，天体力学和变分法，相关成果发表在JEMS，Adv. Math., ARMA，CMP，AIHP-ANL，CVPDE和Nonlinearity等期刊。

邀请人：陈泓旭

数学科学学院

2026年10月28日