Conditions leading to inclination flip and to collision for an encounter of 2000 DG₈ with Saturn. Left: b-plane circles corresponding to post-encounter L′_Sz = 0 (cyan) and to collision with Saturn (red); the black dots come from the numerical check described in the text. Right: corresponding ellipses in the space of initial conditions ω–λ_S; the coloured ellipses are computed with the analytical theory, the black dots come from the numerical check.