Dynamics of the Bianchi IX model near the cosmological singularity

摘要

The mathematical structure of the six dimensional physical phase spaces of the non-diagonal Bianchi IX model is analyzed in the neighborhood of the cosmological singularity. The Bianchi IX model is the realistic prototype for the Belinskii-Khalatnikov-Lifshitz scenario. Critical points of the Hamiltonian equations appearing at infinities are of the non-hyperbolic type, which seems to be a generic feature of considered singular dynamics. The information that can be obtained from the linearized vector field is inconclusive. Making use of the physical Dirac observables as the phase space coordinates lowers substantially the dimensionality of the dynamics arena. Here, using commonly known methods for studying the dynamics may turn out to be satisfactory.