Symbolic dynamics in the symmetric collinear four-body problem

Abstract

In this article we prove the existence of a countable number of ejection-collision orbits for the symmetric collinear four body problem with negative energy. These orbits come out from total collision, pass through a finite sequence of binary and/or simultaneous binary collisions and finally end in total collision. The existence of this family of orbits relies on the existence of the homothetic orbit joining the pair of hyperbolic equilibrium points lying on the total collision manifold and on the knowledge of the flow on the total collision manifold.