Academic Report of School of Mathematical Sciences [2026] No. 104

(Series Report for High-Level University Construction No. 1363)

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

Speaker：Researcher Yu Guowei (Nankai University)

Time：16:30-17:30, Nov. 9, 2026

Location：Room 1420, Huiwen Building, Yuehai Campus, Shenzhen University

Abstract: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.

Speaker Profile：Yu Guowei is a researcher at the Chen Xingshen Institute of Mathematics at Nankai University. He received his Ph.D. in Pure Mathematics from the University of Minnesota in 2013. From 2013 to 2018, he conducted postdoctoral research at the University of Toronto in Canada, Paris IX–Sorbonne University and the Paris Observatory in France, the University of Turin in Italy, and the Mathematical Sciences Research Institute (MSRI) in the United States, focusing on dynamical systems, celestial mechanics, and variational methods. His research findings have been published in journals such as JEMS, Adv. Math., ARMA, CMP, AIHP-ANL, CVPDE, and Nonlinearity.

Faculty and students are welcome to attend!

Invited by: Chen Hongxu

School of Mathematical Sciences

October 28, 2026