Dynamics about the secondary body outside the KAM regime

Characterize the general dynamics of a test particle about the secondary body P2 in the planar circular restricted three-body problem when starting from Keplerian elliptical initial conditions for Jacobi constants outside the near-secondary, high-energy regime where the Kolmogorov–Arnold–Moser (KAM) theorem applies, including identification of invariant structures and long-term behavior.

Background

While KAM theory describes quasi-periodic motion about the primary P1 for small mass ratios and sufficiently irrational frequency ratios, the general motion about the secondary P2 is not understood except very close to P2 at large Jacobi constants.

This gap is central to understanding capture dynamics in realistic energy ranges relevant to the paper’s mechanism and remains explicitly noted as not dynamically understood.

References

However, for motion about P2, the general motion for P starting with Keplerian elliptical initial conditions is not dynamically understood, unless the motion is arbitrarily close to P2 for C sufficiently large where the KAM theorem is valid ([29]).

— Permanent Capture into the Solar System  (2407.09560 - Belbruno et al., 2024) in Section 3 (Modeling: Restricted Three-Body Problem)