Ewa Czuchry, Wlodzimierz Piechocki
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. Critical points of the Hamiltonian equations
appearing at infinities are of the nonhyperbolic type. Specific transformations
of the phase space, including projection into finite region, do not change this
type of criticality which is difficult for investigation by standard analytical
tools. The nonhyperbolicity 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 quite satisfactory.
View original:
http://arxiv.org/abs/1202.5448
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