Structure and fractal nature of the nth weak stability boundary Wn

Determine the structure of the nth weak stability boundary Wn about the secondary body P2 in the planar circular restricted three-body problem and, in particular, ascertain whether Wn has fractal structure and whether trajectories with initial conditions on Wn exhibit chaotic dynamics.

Background

The weak stability boundary Wn comprises initial conditions at the boundary between n-stable and n-unstable cycling around the secondary. Earlier work conjectured that Wn is fractal and that initial conditions on it yield chaotic motion.

Recent results (cited as B24) establish a fractal Cantor-set structure for the limiting set W′ = lim n→∞ Wn on appropriate surfaces of section and energy ranges, but the general structure of Wn itself remains an explicitly noted open problem in the paper.