DYNAMICAL TRAJECTORIES OF SIMPLE DYNAMICAL-SYSTEMS AS GEODESICS - IN SEARCHING FOR INVARIANT CRITERIA OF CHAOS IN GENERAL-RELATIVITY

We will investigate the possibility of describing the chaotic behaviou r of trajectories of simple mechanical systems by means of elementary tools of Riemannian differential geometry. From the curvature properti es of a Riemannian manifold some relevant consequences about stability (instability) properties of its geodesics can be derived. It is impor tant to remark that this information about stability (instability) has an invariant character because they are obtained from the internal Ri emannian geometry. (C) 1998 Elsevier Science Ltd. All rights reserved.