Symplectic Geometry and N-body Problem

辛几何和N体问题

• 批准号: 359698948
• 负责人: Privatdozent Dr. Lei Zhao
• 金额: --
• 依托单位: Lehrstuhl für Analysis und Geometrie
• 依托单位国家: 德国
• 项目类别: Independent Junior Research Groups
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/359698948?language=en
• 关键词: Symplectic; Geometry; body; Problem

The proposal is an extension to the project "Symplectic Geometry and the N-Body Problem". The main purpose is to address diverse problems and research directions of Celestial Mechanics with new methods from symplectic geometry. Within this extension period, we aim to further address the possibility to apply Rabinowitz-Floer theory to study chord problems, in particular consecutive collision orbits in the restricted three-body problems. In the other direction, we wish to address the problem of symmetry in four-body balanced configurations and attempt to obtain results concerning generic finiteness of balanced configurations of N-body problems.

该提案是“辛几何和N体问题”项目的延伸。主要目的是用辛几何的新方法解决天体力学的各种问题和研究方向。在此扩展期内，我们的目标是进一步解决的可能性，应用Rabinowitz-Floer理论研究弦问题，特别是连续碰撞轨道的限制三体问题。在另一个方向，我们希望解决四体平衡配置的对称性问题，并试图获得有关N体问题的平衡配置的一般有限性的结果。