Analysis of the neighborhood of the 2: 1 resonance in the equal-mass three-body problem

We consider the trajectories in the neighborhood of a 2: 1 resonance (in periods of osculating motions of the outer and inner binaries) in the plane equal-mass three-body problem. We identified the zones of motions that are stable on limited time intervals. All of them correspond to the retrograde motions of the outer and inner subsystems. The prograde motions are unstable: the triple system breaks up into a final binary and an escaping component. In the barycentric nonrotating coordinate system, the trajectories occasionally form symmetric structures composed of several leaves. These structures persist for a long time, and, subsequently, the trajectories of the bodies fill compact regions in coordinate space.