  The Bianchi IX cosmological model is analyzed in a generalized uncertainty
principle framework. The Arnowitt-Deser-Misner reduction of the dynamics is
performed and a time-coordinate, namely the volume of the Universe, naturally
arises. Such a variable is treated in the ordinary way while the anisotropies
(the physical degrees of freedom) are described by a deformed Heisenberg
algebra. The analysis of the model (passing through Bianchi I and II) is
performed at classical level by studying the modifications induced on the
symplectic geometry by the deformed algebra. We show that, the Universe can not
isotropize because of the deformed Kasner dynamics, the triangular allowed
domain is asymptotically stationary with respect to the particle (Universe) and
its bounces against the walls are not interrupted by the deformed effects.
Furthermore, no reflection law can be in general obtained since the Bianchi II
model is no longer analytically integrable. This way, the deformed Mixmaster
Universe can be still considered a chaotic system.
