  In the loop quantum cosmology effective dynamics for the vacuum Bianchi type
I and type IX space-times, a non-singular bounce replaces the classical
singularity. The bounce can be approximated as an instantaneous transition
between two classical vacuum Bianchi I solutions, with simple transition rules
relating the solutions before and after the bounce. These transition rules are
especially simple when expressed in terms of the Misner variables: the
evolution of the mean logarithmic scale factor is reversed, while the shape
parameters are unaffected. As a result, the loop quantum cosmology effective
dynamics for the vacuum Bianchi IX space-time can be approximated by a sequence
of classical vacuum Bianchi I solutions, following the usual Mixmaster
transition maps in the classical regime, and undergoing a bounce with this new
transition rule in the Planck regime.
