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}
}