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 The Nature of Computation Cristopher Moore and Stephan Mertens Available now at all good bookstores, or through Oxford University Press http://www.nature-of-computation.org/