Noncollision Singularities in a Planar Four-body Problem
  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. 
Jinxin Xue
math.DS math-ph math.MP