Structure and nature of the finite-cycle weak stability boundary Wn

Determine the dynamical and topological structure of the nth weak stability boundary Wn about the secondary body P2 in the planar circular restricted three-body problem for finite n≥1, including whether Wn is fractal and whether initial conditions on Wn lead to chaotic trajectories.

Background

The weak stability boundary Wn separates n-stable from n-unstable cycling motion about the secondary body and is central to the capture mechanism described. Earlier work suggested fractal features, but rigorous results in B24 address only the infinite-cycle limit W' and not the finite-n case.

The authors explicitly note that the structure of Wn has been an open problem and mention conjectures about fractal and chaotic behavior associated with Wn.