Stability of motion of N-body systems

Complications arising from the non-compact nature of the phase space of N-body systems prevent any asymptotic characterization of chaotic behaviour (since no equilibrium final states can exist). This leads us to revisit some of the old results concerning geodesic stability on Lagrangian manifolds. These cannot be applied directly but may be useful when properly reinterpreted. A method for doing that is described along with some tests of its validity and possible future applications.