Acta Mathematica

Volume 224 (2020)

Number 2

Non-collision singularities in a planar 4-body problem

Pages: 253 – 388



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


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.

Received 14 September 2014

Accepted 30 December 2019

Published 23 June 2020