Phys. Rev. D 50, 819–840 (1994)Invariant chaos in mixmaster cosmologyReceived 17 June 1993; published in the issue dated 15 July 1994 We discuss mathematical aspects of determining local instability parameters by using invariant characteristics of the internal pseudo-Riemannian geometry with the Jacobi metric (in principle, for Hamiltonian dynamical systems). Analytical formulas allowing one to compute the separation rate of nearby trajectories are given and the fundamental difference between the behavior of geodesics in the Riemannian and pseudo-Riemannian spaces carrying Jacobi metrics is stressed. The formalism developed here is used as an invariant tool to detect chaos in general relativity. © 1994 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevD.50.819
DOI:
10.1103/PhysRevD.50.819
PACS:
98.80.Hw
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