and Papaloizou, 2003).

After this change in migration regime,

Saturn’s inward motion continues at a slower, approximately constant rate. After 280 initial orbital period, the migration of Jupiter stops and then it reverses. As they move in opposite directions, Jupiter and Saturn are eventually captured in their mutual 2:3 MMR, at $t=350$. After this event, the two planets migrate outward in parallel. The eccentricity of Saturn stabilizes around 0.012 and that of Jupiter around 0.003. It is worth noticing that the ratio of semi major axes of the two planets does not correspond to a 2:3 ratio of the Keplerian orbital periods. It rather corresponds to a 5:8 ratio. However, by looking at the behavior of the resonant angles, we have checked that the planets are really captured in the 2:3 MMR. The gravity of the disk displaces the mean motion resonances relative to the unperturbed keplerian location.

As we said in the introduction, it is an unsolved issue whether the initial evolution of Saturn, with its runaway migration and fast passage across the 1:2 MMR, plays a role in the subsequent dynamics. For instance, MS01 argue that the capture in the 2:3 MMR is favored by Saturn’s eccentricity being 