Let's just look at your Figure Eight. (Have you succeeded in publishing a paper where it is Fig. 8?) Are those perturbations which don't eject somebody periodic? Do all three bodies follow the same (slightly bent?) orbit, or is the orbit actually blurred? Does it tolerate small nonplanar perturbations? Also, can you get enough decimal places of the aspect ratio of the unperturbed orbit to try an inverse symbolic calculator? Neil B. showed me a picture captioned with a claim it was a quasiperiodic three-body solution, but I can't reconstruct its url. But here's a paper, QUASI-PERIODIC SOLUTIONS OF THE PLANE THREE-BODY PROBLEM NEAR EULER'S ORBITS<http://link.springer.com/article/10.1007%2FBF01230666?LI=true#page-1> that seems to affirm aperiodic immortality, which is what I was after. The idea that such a simple, bounded system can produce endless novelty is a little hard to swallow. --rwg CM> This is a nice question: Richard Montgomery or Alain Chenciner might know the answer. Certainly there are 3-body orbits with different masses that are locally stable. But since the system is Hamiltonian, that just means that the eigenvalues of the Jacobian are on the unit circle, so that perturbations don't grow to first order. When all the nonlinearities are taken into account, I don't know whether there is an open set (or even a dense set) around these orbits that stay in that region forever. Cris On Mar 10, 2013, at 3:02 PM, Bill Gosper wrote: Since there's a (small) continuum of possible perturbations, is there a continuum of possible oscillation periods, mostly incommensurable with the main orbits? More generally, are there concrete examples of "immortal", aperiodic three body systems with comparable masses that never eject one? --rwg Cristopher Moore Professor, Santa Fe Institute