Bianchi IX Chaoticity: BKL Map and Continuous Flow
General Relativity and Quantum Cosmology
2009-11-10 v1 Chaotic Dynamics
Abstract
We analyze the Bianchi IX dynamics (Mixmaster) in view of its stochastic properties; in the present paper we address either the original approach due to Belinski, Khalatnikov and Lifshitz (BKL) as well as a Hamiltonian one relying on the Arnowitt--Deser--Misner (ADM) reduction. We compare these two frameworks and show how the BKL map is related to the geodesic flow associated with the ADM dynamics. In particular, the link existing between the \textit{anisotropy parameters} and the \textit{Kasner indices} is outlined.
Cite
@article{arxiv.gr-qc/0401086,
title = {Bianchi IX Chaoticity: BKL Map and Continuous Flow},
author = {Giovanni Imponente and Giovanni Montani},
journal= {arXiv preprint arXiv:gr-qc/0401086},
year = {2009}
}
Comments
4 pages, no figures, proceedings of Frontier Science 2003, to appear on Physica A