Oscillatory orbits in the restricted planar four body problem

Abstract

Abstract The restricted planar four body problem describes the motion of a massless body under the Newtonian gravitational force of other three bodies (the primaries), and the motion of the primaries gives us general solutions of the three body problem. A trajectory is called oscillatory if it goes arbitrarily faraway but returns infinitely many times to the same bounded region. We prove the existence of such type of trajectories provided the primaries evolve in suitable periodic orbits.