Ancient Dynamics in Bianchi Models: Approach to Periodic Cycles

Details Ancient Dynamics in Bianchi Models: Approach to Periodic Cycles Ancient Dynamics in Bianchi Models: Approach to Periodic Cycles

2010-04-12

arxiv.org/abs/1004.1989v3

Commun.Math.Phys.305:59-83,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Minor corrections and clarifications throughout the text, according to referee's suggestions

Scientific paper

10.1007/s00220-011-1248-3

We consider cosmological models of Bianchi type. In particular, we are interested in the alpha-limit dynamics near the Kasner circle of equilibria for Bianchi classes VIII and IX. They correspond to cosmological models close to the big-bang singularity. We prove the existence of a codimension-one family of solutions that limit, for t to negative infinity, onto a heteroclinic 3-cycle to the Kasner circle of equilibria. The theory extends to arbitrary heteroclinic chains that are uniformly bounded away from the three critical Taub points on the Kasner circle, in particular to all closed heteroclinic cycles of the Kasner map.

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