Distribution of W′ (infinite-cycle weak stability boundary) capture points about the secondary

Characterize the distribution of the points of W′ (the weak stability boundary for infinitely many cycles) around the secondary body P2 in the planar circular restricted three-body problem, including their spatial arrangement and density on relevant surfaces of section.

Background

The paper shows that W′ is a fractal Cantor set on surfaces of section for certain Jacobi energies and that it bounds a region of stable infinite cycling. Although the set’s qualitative structure is established, the authors state that the distribution of its points around the secondary is unknown.

They note that computing Wn for high n is numerically demanding and that identifying points of W′ (and the subset corresponding to permanent capture from outside H2) would be even more challenging, motivating this open problem.