北航数学论坛学术报告

--分析与偏微分方程讨论班

Hyperbolic motion in the Newtonian N-body problem with arbitrary limit shape

Andrea Venturelli

（Laboratoire de Mathématiques d'Avignon, France）

报告时间：21:00-22:00，2022-1-17 (星期一)

Zoom：829 6231 5870， Password：452151

会议链接： https://us02web.zoom.us/j/82962315870

摘要：We prove for the N-body problem the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. The energy level h>0 of the motion can also be chosen arbitrarily. Our approach is based on the construction of a global viscosity solutions for the Hamilton-Jacobi equation H(x,du(x))=h. Our hyperbolic motion is in fact a calibrating curve of the viscosity solution. The presented results can also be viewed as a new application of Marchal's theorem, whose main use in recent literature has been to prove the existence of periodic orbits. It is a joint work with Ezequiel Maderna.

报告人简介：Andrea Venturelli，法国Université d´Avignon教授，研究领域包含动力系统、变分法和N体问题等，在Ann. of Math. , Arch. Rat. Mech. Anal.，CVPDE等著名杂志上发表多篇论文。