  We consider the evolution of a dilute Bose-Einstein condensate in an optical
trap formed by a doughnut laser mode. By solving a one dimensional
Gross-Pitaevskii equation and looking at the variance and the statistical
entropy associated with the position of the system we can study the dynamical
behavior of the system. It is shown that for small condensates nonlinear
revivals of the macroscopic wave function are expected. For sufficiently large
and dense condensates irreversible dynamics takes place for which revivals of
regular dynamics appear as predicted in [9]. These results are confirmed by a
two dimensional simulation in which the scales of energy associated with the
two different directions mimic the experimental situation.
