M. Szydlowski et A. Krawiec, DESCRIPTION OF CHAOS IN SIMPLE RELATIVISTIC SYSTEMS, Physical review. D. Particles and fields, 53(12), 1996, pp. 6893-6901
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.