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800 keV above yrast, which represents the onset of rotational damping. Above 
doi:10.1016/0375-9601(90)90553-Z 
Copyright © 1990 Published by Elsevier Science B.V. All rights reserved.
Chaotic behaviour and oscillating three-volumes in Bianchi IX universes
Received 19 March 1990;
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Abstract
Previous numerical studies of vacuum Bianchi IX cosmologies unwittingly contained “matter” having negative energy density, thereby causing erratic oscillations in the three-volume and apparent chaotic behavior of the principal axes. The behaviour with physically acceptable positive or zero energy densities shows the expected monotonically declining three-volume. We show further that the maximal Liapunov characteristic exponent of the phase flow is zero with respect to the time variable that is usually used in investigating this model. Despite this, the deterministic model is unpredictable (the entropy per cycle is large and positive) with respect to the number of Kasner epochs comprising each major cycle.
