  We numerically study a rotating Bose-Einstein condensate placed transiently
over the critical rotation frequency i.e. in a regime where the rotation
frequency is larger than the radial frequency of the confinement. We study the
reversibility of this process depending on the strength of the interactions and
the presence of vortices. We find that the reversibility is broken by the
interactions in the absence of vortices but systematically quasi-restored in
the presence of a single vortex.
