Is there a theorem that guarantees that in the case of compact and Lyapunov stable n-body orbits with Newton potential, the trajectory of each particle must be smooth? This seems very plausible but I haven't found a proof or a counter-example in the literature on the n-body problem.
Note 1: First, I must say that I am only interested in solutions that are compact(i.e. free from collisions and unbounded orbits) and where all masses are equal. By Lyapunov stable I mean that a slight perturbation of the initial conditions results in a compact solution that has the same shape(i.e. belongs to the same homotopy class).
Note 2: I suspect that if this theorem is true, then it holds for all potentials of the form $r^{-a}$ where $a>1$ and that it would also hold true for the case when the masses are not equal.