INVARIANT CHAOS IN MIXMASTER COSMOLOGY

Citation
M. Szydlowski et J. Szczesny, INVARIANT CHAOS IN MIXMASTER COSMOLOGY, Physical review. D. Particles and fields, 50(2), 1994, pp. 819-840
Citations number
47
Categorie Soggetti
Physics, Particles & Fields
ISSN journal
05562821
Volume
50
Issue
2
Year of publication
1994
Pages
819 - 840
Database
ISI
SICI code
0556-2821(1994)50:2<819:ICIMC>2.0.ZU;2-G
Abstract
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.