INVARIANT CHAOS IN MIXMASTER COSMOLOGY

We discuss mathematical aspects of determining local instability param eters by using invariant characteristics of the internal pseudo-Rieman nian geometry with the Jacobi metric (in principle, for Hamiltonian dy namical systems). Analytical formulas allowing one to compute the sepa ration rate of nearby trajectories are given and the fundamental diffe rence between the behavior of geodesics in the Riemannian and pseudo-R iemannian spaces carrying Jacobi metrics is stressed. The formalism de veloped here is used as an invariant tool to detect chaos in general r elativity.