The local instability of simple relativistic systems

The invariant criterion of local instability of geodesic motion in terms of Riemannian (pseudo-Riemannian) geometry is proposed. The property of sensitive dependence on initial conditions is formulated as the local instability of nearby geodesics. In the study of sectional curvature, the bivector formalism is applied. We demonstrate the effectiveness of our method of investigating local instability in the behaviour of simple relativistic mechanical systems.