Qualitative approach of the general vacuum Bianchi VI and VII cosmological models near the singularity

We first show that the chaos-generating terms are absent from the vacuum field equations in the case of the general Bianchi VI and VII cosmological models. According to recent studies, this proves that the Kasnerian metric is a general solution for these models in the neighborhood of the initial singularity. Then, using a method developed by Jantzen, we reduce the field equations to a nonautonomous system of order two. A numerical integration leads to the explicit four-parameter asymptotic form of a general solution, which is indeed Kasnerian in the canonical invariant basis.