USING GPUS AND THE PARAMETERIZATION METHOD FOR RAPID SEARCH AND REFINEMENT OF CONNECTIONS BETWEEN TORI IN PERIODICALLY PERTURBED PLANAR CIRCULAR RESTRICTED 3-BODY PROBLEMS

The model’s three-part solution mirrors the paper’s method: (i) it derives the layer mapping property from the invariance F(W(θ,s)) = W(θ+ω, λ s), consistent with the paper’s globalization identities and the statement F^k(Un)=Un+k, F^k(Sn)=Sn−k (see eqs. (11), (14)–(15) and the layer mapping discussion) ; (ii) it proves the parity reduction that any heteroclinic point can be shifted by some k to lie in a pair (Un,Sn) or (Un,Sn−1), exactly as argued in the paper (eq. (21) and the ensuing cases) ; (iii) it derives the pull-back/push-forward derivative formulas and assembles the Jacobian for a damped Newton refinement, matching the paper’s eqs. (36)–(39) and Newton step (45) . The only differences are expositional: the model states a clean separation assumption for excluding intersections inside the fundamental domains (the paper notes this empirically) , and it cites standard Newton–Kantorovich conditions for local convergence (the paper uses a practical damped Newton with α chosen by trial-and-error) .