Hi Warren. I think that the circular orbit is a minimum of the action for 1/r^a where a > 3, but is dynamically unstable. So I don't think being a minimum of the action (as opposed to a saddle point) is associated with dynamical stability. But I haven't thought about this in a while... Cris On Mar 11, 2013, at 1:15 PM, Warren D Smith wrote:
If it can be shown that some N-body (or other Hamiltonian system) periodic solution is an action minimum, does that prove a stability claim? And by minimum I mean strict local minimum within some space of small-perturbations.
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/