NUMERICAL STUDY OF INITIALLY EXPANDING MIXMASTER UNIVERSES

Numerical studies by Burd et al. (1989) and Hobill et al. (1989) indicate that the mixmaster universe is not chaotic since the Liapunov exponents computed from its dynamics by the standard formula vanish. Burd et al. use a non-standard short-time definition of the exponents to indicate that mixing is still present. Here it is found that mixmaster universes regarded as trajectories in a minisuperspace exhibit a quasichaos if the trajectory passes through a maximum of expansion despite the vanishing Liapunov exponents. It is shown that the frequency of bounces off the minisuperspace potential and the importance of the potential corners increase near the maximum of expansion. Trajectories with small but finite differences in their initial conditions exhibit qualitatively distinct evolutions in the direction of the big crunch. This phenomenon is not found for initially collapsing universes.