On the dynamics and topology of the elliptic rectilinear restricted 3-bodyproblem

We study a symmetric collinear restricted 3-body problem, where the equal m ass primaries perform elliptic collisions, while a third massless body move s in the line between the primaries, during the time between two consecutiv e elliptic collisions. After desingularizing binary and triple collisions, we prove the existence of a transversal heteroclinic orbit beginning and en ding in triple collision. This orbit is the unique homothetic orbit that th e problem possess. Finally, we describe the topology of the compact extende d phase space.