  We study the Hamiltonian dynamics of the dust-Bianchi IX universe in dust
time gauge. This model has three physical metric degrees of freedom, with
evolution determined by a time-independent physical Hamiltonian. This approach
gives a new physical picture where dust-Bianchi IX dynamics is described by
oscillations between dust-Kasner solutions, rather than between vacuum-Kasner
solutions. We derive a generalized transition law between these phases, which
has a matter component. Sufficiently close to a singularity, we show that this
law reduces to the vacuum Belinski-Khalatnikov-Lifshitz map. We include an
analysis with dust and a scalar field. Lastly, we describe a path integral
quantization using the dust-time physical Hamiltonian and derive an effective
action for the dust-Kasner model by integrating out the anisotropy degrees of
freedom.
