  The mathematical structure of higher-dimensional physical phase spaces of the
nondiagonal Bianchi IX model is analyzed in the neighborhood of the
cosmological singularity by using dynamical system methods. Critical points of
the Hamiltonian equations appear at infinities and are of a nonhyperbolic type,
which is a generic feature of the considered singular dynamics. The reduction
of the kinematical symplectic 2-form to the constraint surface enables the
determination of the physical Hamiltonian. This procedure lowers the
dimensionality of the dynamics arena. The presented analysis of the phase space
is based on canonical transformations. We test our method for the specific
subspace of the physical phase space. The obtained results encourage further
examination of the dynamics within our approach.
