We analyze the semiclassical and quantum behavior of the Bianchi IX Universe
in the Polymer Quantum Mechanics framework, applied to the isotropic Misner
variable, linked to the space volume of the model. The study is performed both
in the Hamiltonian and field equations approaches, leading to the surprising
result of a still singular and chaotic cosmology, whose Poincar\'e return map
asymptotically overlaps the standard Belinskii-Khalatnikov-Lifshitz one. In the
quantum sector, we reproduce the original analysis due to Misner, within the
revised Polymer approach and we arrive to demonstrate that the quantum numbers
of the point-Universe still remain constants of motion. This issue confirms the
possibility to have quasi-classical states up to the initial singularity. The
present study clearly demonstrates that the asymptotic behavior of the Bianchi
IX Universe towards the singularity is not significantly affected by the
Polymer reformulation of the spatial volume dynamics both on a pure quantum and
a semiclassical level.Comment: 25 pages, 10 figures. v2: more discussions/clarification adde