CONTACT GEOMETRY IN THE RESTRICTED THREE-BODY PROBLEM – MINI-COURSE LECTURE NOTES –

The uploaded paper’s main theorem (Theorem M) states that for the regularized spatial CR3BP, the bounded energy hypersurface Σ_c carries an adapted open book with pages D* S^2 and monodromy τ^2 for c < H(L1), and with pages the boundary connected sum D* S^2 \natural D* S^2 and monodromy τ_1^2 ∘ τ_2^2 for c in a small window above H(L1) when µ<1; the binding is the planar problem Σ^P_c (explicitly RP^3 in the statement) . The contact-type property in the same low-energy range is summarized as Theorem K and attributed to AFvKP (planar) and CJK (spatial) . The construction proceeds by the polar-angle map π(x)=Arg(q_3+ip_3) off the planar set, showing ω_p(X_H)≥0 with equality only on the binding, together with an interpolation near the collision locus to the geodesic open book; these are explained in detail (equation (7.13) and the collision-neighborhood discussion) . The candidate solution reproduces exactly this architecture and the same mapping-class identification for the return map, invoking Seidel’s result on π_0(Symp_c(D* S^2)) and the rotating Kepler model; this aligns with Theorem M’s monodromy description. One clarification the candidate makes is that above H(L1) the planar binding is RP^3#RP^3; this matches the paper’s Moser-regularization discussion of the planar problem, even though Theorem M’s one-line binding description mentions only RP^3 . Overall, both the paper (as lecture notes summarizing [MvK]) and the candidate give the same construction and identifications; the notes explicitly defer technical estimates near collisions to [MvK], which the candidate also references.