Note that this section shows a large chaotic zone in the middle. We have stable quasi-periodic trajectories above and below this zone along with islands of stability in between which correspond to a resonance with Saturn i.e. the rotation period, and its revolution period are in the ratio of small natural numbers. In this mode of rotation the orbital period of Saturn assumes quasi-periodicity and so the motion is stable. In this zone the motion of Hyperion becomes more predictable.

The central zone itself confirms that Hyperion rotates chaotically. With this insight, when we return to the original problem, we find that in the chaotic zone, the fixed orientation of Hyperions axis is unstable. Therefore the evolution of Hyperion would probably involve two stages. First its axis of rotation would be brought into the orientation described above, but the moment it entered the chaotic zone it would start tumbling.

Recent photographs taken by the Voyager spacecraft confirm that Hyperion is tumbling.