Statistical evolution of the maximum distance from the Sun reached in the time interval [T,0],obtained by backward integrating a sample of simulated comets for 150 000 years. The initial epoch is identified by T = 0, the final one by T = −150 000 years. The sample of simulated comets is defined by 1000 initial conditions regularly spaced on ż₀, with |ż₀−ż_∗| ≤ 10^-7 (the other initial conditions are the same as ξ_∗). At any given value of the time T, we represent the percentage ofsimulated comets whose maximum distance from the Sun in [T,0] is smaller than 30 AU, between 30 AU and 50 AU, between 50 and 100 AU, and larger than 100 AU. We also represent the percentage ofsimulated comets that passed under Jupiter’s Roche limit ( identified as collisions).