Surface of a section in the (Γ′,X) plane of the Hamiltonian (2). The black line shows the positions of the family of elliptic fixed points (the hyperbolic family exists for larger values of X and is not displayed here). The red line shows the intersection of the separatrix with the Y = 0 plane for each value of Γ′. The coloured dots show the intersection of the trajectories emanating from the initial conditions of the posterior summarised in Sect. 2 and the (Γ′, X) plane, for Kepler-1972 (this paper) and Kepler-1705 (Leleu et al. 2021b).