$n$ 体问题在所有维度中不存在无限自旋
No infinite spin in the $n$-body problem in all dimensions
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中文总结 AI 辅助
本文在无孤立中心构型收敛假设下，证明所有维度中 $n$ 体问题的任意碰撞解或抛物解均不存在无限自旋，推广了 Moeckel-Montgomery 的平面结果。
中文摘要 AI 辅助
在平面 $n$ 体问题中，Moeckel 和 Montgomery \cite{MM25} 证明了当约化并归一化的构型收敛到孤立中心构型时，总碰撞解不存在无限自旋。沿用他们的方法，多位作者在相同假设（即约化并归一化的构型收敛到孤立中心构型）下，分别将这一结论推广到平面情形中的部分碰撞解和抛物解，以及空间情形中的总碰撞解。本文在无此假设的情况下，证明了在所有维度中，任何碰撞解或抛物解都不存在无限自旋。
英文摘要
In the planar $n$-body problem, Moeckel and Montgomery \cite{MM25} showed that there is no infinite spin for total collision solutions, when the reduced and normalized configuration converges to an isolated central configuration. Following their approach, generalizations have been obtained for partial collision solutions and parabolic solutions in the planar case, and for total collision solutions in the spatial cases by various authors, all under the same assumption that the reduced and normalized configuration converges to an isolated central configuration. Here we prove there is no infinite spin for any collision or parabolic solution in all dimensions without such an assumption.
发表机构
- Nankai University（南开大学）
机构由 AI 辅助整理，请以论文原文为准。
