报告题目：Frozen planet orbits: a variational approach

报 告 人：Stefano Banangini  博士（都灵大学）

报告时间：2025年9月12日（星期五）10:30- 11:30

报告地点：数学科学学院115（大报告厅）   

校内联系人： 赵磊 教授   联系方式：84708351-8625

报告摘要：In this talk, I will discuss the existence of a family of periodic orbits,called frozen planet orbits, for a 1−d atomic model. We have n-electrons moving on a half-line with the nucleus sitting at the origin. Electrons are subject to reciprocal electric attraction/repulsion while the nucleus is xed.We will prove that, for any period T > 0, there exists a periodic solution of the following form. The rst electron keeps bouncing on the nucleus whereas the others oscillate synchronously, without collisions. We call these trajectories frozen planet orbits, from a Hamiltonian perspective they are collisional periodic brake solutions.If time permits, I will discuss a connection between a limit system, in which the negative charges disappear, and billiard dynamics. This is a joint work with G. Canneori and S. Terracini.

References Frozen planet orbits for the n−electron atom, Baranzini S.,Canneori G.M., Terracini S., to appear in Communications in Mathematical Physics.