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 behaviour of trajectories of simple mechanical systems by means of elementary tools of Riemannian differential geometry. From the curvature properties of a Riemannian manifold some relevant consequences about stability (instability) properties of its geodesics can be derived. It is important to remark that this information about stability (instability) has an invariant character because they are obtained from the internal Riemannian geometry.