【online】Some recent progress on non-collision singularities in Newtonian N-body problems
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题目: Some recent progress on non-collision singularities in Newtonian N-body problems
时间: 2021年11月18日 16:00 -17:00
报告方式: 腾讯会议 ID：827 244 037 密码：123456
摘要：In Newtonian N-body problems, the existence of non-collision singularities, which means there are orbits of the system exhibiting the peculiar feature that some bodies would escape to infinity in finite time with velocities of infinite large without the occurrence of collisions (two or more bodies occupying the same point in the physical space), has been long speculated for N>=4. This was commonly known as the Painleve conjecture and has been recently resolved by J. Xue [Acta Math 2020]. In this talk we would review several existing models that allow the existence of non-collision singularities and introduce a new model in a planar 4-body problem. Using the method developed by Xue in [Acta Math 2020], with numeric assistant checking certain non-degeneracy properties of the system, we show the existence of non-collision singularities in this new configuration.