报告题目：限制性一中心二体问题的Sundman-Sperling估计

报告时间：2024-04-24   16:30-17:30

报 告 人：刘磊  副教授(山东大学)

报告地点：理学院东北楼四楼报告厅（404）

Abstract：In the past two decades, since the discovery of the figure-8 orbit by Chencinerand Montgomery, the variational method has becameone of the most popular tools for constructing new solutions of the N-body problem and its extended problems. However, finding solutions to the restricted three-body problem, in particular, the two primaries form a collision Kepler system, remains a great difficulty. One of the major reasons is the essential differences between two-body collisions and three-body collisions. In this paper, we consider a similar three-body system with less difficulty, i.e.the restricted one-center-two-body system, that is involving a massless particle and a collision Kepler system with one body fixed. It is an intermediate system between the restricted three-body problem and the two-center problem. By an in-depth analysis of the asymptotic behavior of the minimizer, and an argument of critical and infliction points, we prove the Sundman-Sperling estimates near the three-body collision for the minimizers. With these estimates, we provide a class of collision-free solutions with prescribed boundary angles. Finally, under the extended collision Kepler system from Gordon, we constructed a family of periodic and quasi-periodic solutions.