The problem of orbit stability in a central gravitational potential field is quite old, and probably began just after Newton discovered the universal gravitation law. The KAM (Kolmogorov, Arnold, Moser) theorem
gave a workable approximate solution to the problem. The prediction of KAM theorem is that orbitating bodies whose orbit period ratio is irrational remain stable, while orbits whose revolution rate is of the type m/n (m, n integers) are swept away. This for example explains the "holes" in the asteroid belt between Mars and Jupiter. The paper referred by Slashdot gives a beautiful simulation result of a very complex problem of mathematical physics, however we should also remember that the authors of the KAM theorem obtained the solution using nothing but pencil and paper about fifty years ago...It is however wonderful to see how modern simulation and visualization methods can give new insight to old ideas!