  The implications of a Generalized Uncertainty Principle on the Taub
cosmological model are investigated. The model is studied in the ADM reduction
of the dynamics and therefore a time variable is ruled out. Such a variable is
quantized in a canonical way and the only physical degree of freedom of the
system (related to the Universe anisotropy) is quantized by means of a modified
Heisenberg algebra. The analysis is performed at both classical and quantum
level. In particular, at quantum level, the motion of wave packets is
investigated. The two main results obtained are as follows. i) The classical
singularity is probabilistically suppressed. The Universe exhibits a stationary
behavior and the probability amplitude is peaked in a determinate region. ii)
The GUP wave packets provide the right behavior in the establishment of a
quasi-isotropic configuration for the Universe.
