The Broucke-Hénon orbit and the Schubart Orbit in the planar three-body problem with equal masses

英文摘要：

In this paper, we study the variational properties of two special orbits: the Schubart orbit and the Broucke-Hénon orbit. We show that under an appropriate topological constraint, the action minimizer must be either the Schubart orbit or the Broucke-Hénon 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.