Geometry of transit orbits in the periodically-perturbed restricted three-body problem

The paper proves that the monodromy map Λ, in a symplectic eigenbasis near an elliptic–hyperbolic fixed point, is the time‑T map of a quadratic Hamiltonian H̃2 = λ̃ q1 p1 + (ν̃/2)(q2^2 + p2^2) with λ̃ = (ln σ)/T and ν̃ = ψ/T, and uses this to reproduce the Conley–McGehee transit/non‑transit geometry in the discrete setting; see Sections 3–4 and Appendix B , and the classification via q1 p1 = const and lines p1 − q1 = ±c in Section 2.5 . The candidate solution reconstructs the same H̃2 and the same transit/non‑transit classification, adding a monotonicity check of D_k and explicit small‑parameter choices. Aside from a minor, nonessential over‑tight bound on coordinates when choosing c and h, the model’s argument matches the paper’s logic. Both appeal to standard persistence to carry the linear picture to the nonlinear stroboscopic map (the paper cites Moser/Wiggins, the model cites HPS/Carr), so the overall conclusions agree .