Local integrability of the mixmaster model

In this paper we study the mixmaster universe whose evolution is described by a polynomial Hamiltonian. We show that this model is locally integrable. The Taub solutions form an integrable subsystem. We show that there are no solutions of the mixmaster universe asymptotic to a partially isotropic gravitational collapse, that is, a collapse where two of the metric coefficients are always equal, other than the Taub solutions.