DESCRIPTION OF CHAOS IN SIMPLE RELATIVISTIC SYSTEMS

Chaos is investigated in the context of general relativity and gravita tion. We show how quantitative and global measures of chaos can be obt ained from qualitative and local ones. After averaging-first, over all two-directions, and second, along the trajectory-the rate of separati on of nearby trajectories (Lyapunov-like exponents) can be obtained. T his gives us a tool to the invariant chaos description. The sign of th e Ricci scalar serves as a criterion of the local instability in simpl e mechanical systems (systems with a natural Lagrange function). We al so show how to reduce relativistic simple mechanical systems to the cl assical ones. Timelike and null geodesics in multi-black-hole cosmolog ical spacetimes are considered. The role of relativistic systems in ge neral relativity is emphasized.