Orbit's Structure in the Isosceles Rectilinear Restricted Three-Body Problem

The isosceles rectilinear restricted three-body problem can be considered as the Sitnikov's problem with eccentricity one or, as the isosceles problem when the central mass is zero and the primaries move having consecutive elliptic collisions. We compactify the phase space and analyze the flow on their boundary. This allows us to separate the phase space into different regions depending on the kind of orbits.