Distribution of weak capture points on the infinite-cycle boundary W'

Determine the spatial distribution, in Sun-centered (Y1, Y2) coordinates, of the points comprising the infinite-cycle weak stability boundary W' around the secondary body P2 (the Sun) in the planar circular restricted three-body problem with primary PMW, including characterization of how these Cantor sets are arranged and their density.

Background

The set W' is proven in B24 to be a Cantor-like fractal on surfaces of section and forms the boundary of a region S where infinitely stable cycling occurs. Although the existence and qualitative structure are established, the specific distribution of W' points in physical space remains unknown.

The authors emphasize that computing Wn for large n is difficult and that discerning the Cantor points of W' would be numerically challenging, motivating the explicit statement of this unknown.