Persistence of permanent capture regions under more realistic modeling

Establish the existence of permanent weak capture regions in the Solar System under a more realistic dynamical model than the simplified planar circular restricted three-body problem that approximates the Milky Way’s gravitational field by a point mass at the Galactic Center. Specifically, determine whether permanent weak capture sets persist when using a more detailed Galactic potential and three-dimensional motion for the Sun and test particle.

Background

The paper develops a theoretical mechanism for permanent weak capture using a simplified model: the planar circular restricted three-body problem with the Sun (secondary), a point-mass representation of the Galaxy at the Galactic Center (primary), and a test particle. Under this approximation, the authors identify fractal weak capture sets and associated dynamics.

They explicitly note that extending the analysis to a more realistic setting is not described. Nevertheless, they conjecture that analogous permanent capture regions would still exist beyond the simplifications (e.g., non-planar motion and more accurate Galactic tidal models).