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Non-collision singularities in a planar 4-body problem

Jinxin Xue Yau Mathematical Sciences Center and Department of Mathematics, Tsinghua University, Beijing, China

TBD mathscidoc:2203.43001

Acta Mathematica, 224, (2), 253-388, 2020.6
In this paper, we show that there is a Cantor set of initial conditions in the planar 4‑body problem such that all four bodies escape to infinity in a finite time, avoiding collisions. This proves the Painlevé conjecture for the 4‑body case, and thus settles the last open case of the conjecture.
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@inproceedings{jinxin2020non-collision,
  title={Non-collision singularities in a planar 4-body problem},
  author={Jinxin Xue},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220310102731288247913},
  booktitle={Acta Mathematica},
  volume={224},
  number={2},
  pages={253-388},
  year={2020},
}
Jinxin Xue. Non-collision singularities in a planar 4-body problem. 2020. Vol. 224. In Acta Mathematica. pp.253-388. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220310102731288247913.
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