Oscillatory Motions in the Restricted 3-Body Problem: A Functional Analytic Approach

Jaime Paradela, Susanna Terracini

uncertainhigh confidence

Category: math.DS
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves the existence of oscillatory motions in the RI3BP for Lebesgue-almost every angular momentum G and explains how to obtain multibump homoclinics via a variational/topological-degree approach; it also recalls that all 16 Chazy past/future combinations are known only for |G| large from earlier work. It does not claim nor prove that all 16 combinations occur for a.e. G. Hence the stronger statement posed in the solver question remains unproved, aligning with the model’s assessment that it was likely open as of 2022–12–12. See the abstract and outline asserting oscillatory motions for a.e. G, and the citation of the large-|G| “all pairs” result (Theorem 1.3 quoting GPSV) .

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

This work gives a first complete analytic proof of oscillatory motions for a.e. angular momentum in the RI3BP, outside perturbative regimes. It blends a renormalized variational principle, Struwe’s monotonicity trick, a Hofer-inspired degree argument, and a parabolic Lambda lemma to create multibump homoclinics. The results imply non-integrability and positive entropy for a.e. G. The techniques are robust and of broader interest. Minor clarifications would further enhance accessibility.