Wisdom Seen by Carl Murray

"The breakthrough came in 1981 when Jack Wisdom, then a PhD student at the California Institute of Technology, developed a new numerical method for studying the motion of asteroids at resonance. Wisdom [Another pertinent name! -LB] knew about chaotic dynamics, and in particular how to derive "mappings" to speed up the numerical work. Given the state of a system at a certain time, a could give a precise, algebraic method for calculating the at some fixed time interval later. He still had to carry out the mapping on a computer, but using the mapping speeded up calculations 1000 times. As part of his thesis work, derived a mapping to study motion at the 3:1 Jovian resonance. He showed that asteroids, moving under the gravitational effects of the Sun and Jupiter, at this resonance could undergo large,unpredictable changes in their orbits. Such orbits were  chaotic.Wisdom  went on to show that these orbits crossed the orbit of Mars and would eventually impact or be scattered by the planets."

A little ahead in the same note we get:

"In 1984, Jack Wisdom and Stan Peale working at the University of California, Santa Barbara, and Francois Mignard of C E R G A, Grasse, published a classic paper in which they showed that the simple theory worked out for satellite rotations does not apply to Hyperion, because it is distinctly nonspherical. Hyperion's rotation is certainly not synchronous, but neither is it regular; it is chaotic. Furthermore, Wisdom, Peale and Mignard showed that Hyperion is also "attitude unstable" , which means that its spin axis is not fixed and the satellite is tumbling in space as well as rotating chaotically. In normal circumstances, the satellite orbit would become more circular and eventually the chaotic behaviour would disappear, but, ironically, tiny Hyperion is locked in an apparently stable 4:3 orbit-orbit resonance with the massive satellite of Saturn, Titan. This forces Hyperion's orbit to be eccentric rather than circular, so the chaos persists, resulting in a satellite with a chaotic spin but a regular orbit. "
Taken from Carl Murray.

This is how Murray ends his note:

"Laskar's results still have to be confirmed by integrating the full equations of motion, but this will have to wait until the next generation of supercomputers arrives. Meanwhile, we can take comfort from the fact that his work does not imply that orbital catastrophe awaits our planet, only that its future path is unpredictable. It seems likely that the Solar System is chaotic but nevertheless confined, although we have yet to prove it.More than 300 years after the publication of Newton's Principia, we are still struggling to understand the full implications of his square law of gravity. We have begun to view our system of chaos in a light that is revealing the true intricacies of its majestic clockwork."