Bianchi IX Chaoticity: BKL Map and Continuous Flow

Details Bianchi IX Chaoticity: BKL Map and Continuous Flow Bianchi IX Chaoticity: BKL Map and Continuous Flow

2004-01-20

arxiv.org/abs/gr-qc/0401086v1

Physica A338 (2004) 282-285

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages, no figures, proceedings of Frontier Science 2003, to appear on Physica A

Scientific paper

10.1016/j.physa.2004.02.053

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.

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