Representation of the maximum distance from the Sun reached in the interval [T,T₀] by orbits with initial conditions on a grid of 500 × 500 initial conditions regularly spaced on (ẋ,ż) (the axes in the picture represent (ẋ₀−ẋ_∗,ż₀−ż_∗); the other initial conditions are the same as comet 67P), for |T| = 500 yrs (top panels). The colour scale represents the maximum distance, so that yellow means distances larger than 20 AU (top-left panel) or 30 AU (top-right panel). The top-right panel is a zoom-in of the top-left panel. The curves in the pictures are clearly correlated to the ridges of the FLI (see Fig. 1); the topology detected in the zoomed-in picture indicates that we can continue the exploration by fixing the value of ẋ₀ = ẋ_∗: in the bottom panels we represent the maximum distance from the Sun reached in the interval [T,T₀] by 10 000 orbits with all the initial conditions equal to ξ_∗, except for ż₀, and times T = 1000 (bottom-left panel) and T = 2000 (bottom–right panel).