English

Noncollision Singularities in a Planar Four-body Problem

Dynamical Systems 2020-01-31 v3 Mathematical Physics math.MP

Abstract

In this paper, we show that there is a Cantor set of initial conditions in the planar four-body problem such that all four bodies escape to infinity in a finite time, avoiding collisions. This proves the Painlev\'{e} conjecture for the four-body case, and thus settles the last open case of the conjecture.

Keywords

Cite

@article{arxiv.1409.0048,
  title  = {Noncollision Singularities in a Planar Four-body Problem},
  author = {Jinxin Xue},
  journal= {arXiv preprint arXiv:1409.0048},
  year   = {2020}
}
R2 v1 2026-06-22T05:44:28.420Z