Computer assisted proofs for transverse heteroclinics by the parameterization method

The uploaded paper explicitly proves the existence of transverse heteroclinic cycles between the L1 and L2 planar Lyapunov families in the lunar Hill problem at Jacobi constants C = 2.5 and C = 4 (Theorem 4.3), using validated Fourier–Taylor parameterizations of invariant manifolds and a rigorously bounded Chebyshev BVP solver; see the theorem statement and accompanying details and figures in the paper’s Section 4.2 and Figures 6–7 . The model’s solution reduces to the same μ = 0 Hill system (their Eq. (5) with λ1 = 0, λ2 = 3) and Jacobi integral, matching the paper’s formulation of the HRFBP/Hill problem , and then cites the same type of computer-assisted a‑posteriori result to conclude existence and transversality of the heteroclinic connections. A minor divergence is that, in the μ = 0 case, the paper infers the reverse-direction connection by reversibility symmetry (rather than validating it separately), whereas the model text states that both directions are validated directly; nonetheless, Theorem 4.3 is exactly what the model invokes, so the two are in substantive agreement .