On the identification of multiple close encounters in the planar circular restricted three-body problem

We describe a technique which allows us to numerically detect orbits of the planar circular restricted three-body problem with multiple close encounters with the secondary mass for values of the Jacobi constant C < 3 + μ2 - 4μ. We find that these orbits are organized in structures which, on Poincaŕe surfaces of sections, appear as a hierarchy of lobes. The detection of multiple close encounters has implications in cometary dynamics as well as in the study of steroids with potential impact risk with the Earth.