The Broucke-H\'enon orbit and the Schubart Orbit in the planar   three-body problem with equal masses
  In this paper, we study the variational properties of two special orbits: the Schubart orbit and the Broucke-H\'{e}non orbit. We show that under an appropriate topological constraint, the action minimizer must be either the Schubart orbit or the Broucke-H\'{e}non orbit. One of the main challenges is to prove that the Schubart orbit coincides with the action minimizer connecting a collinear configuration with a binary collision and an isosceles configuration. A new geometric argument is introduced to overcome this challenge. 
Wentian Kuang, Tiancheng Ouyang, Zhifu Xie, Duokui Yan
math.DS