states.

A large amount of work has been done on equilibrium states of Bianchi models. Wainwright, Ellis and collaborators have studied equilibrium points of homogeneous models for General Relativity with perfect fluid, tilted or not and found asymptotically isotropic solutions. A good summary of their work is [@WaiEll97]. They use Hubble-normalized variables to study the dynamics of Einstein field equations. The normalisation factor is the Hubble parameter and the equation allowing to show that variables are normalized is the generalized Friedman equation. In this paper we will also consider normalized variables but we will use the Hamiltonian as normalisation factor. The expression for Hamiltonian will be the constraint from which we deduce that variables are normalized. More recently Barrow and Kodama[@BarKod01; @BarKod00] have examined the influence of topology on isotropy and flatness of the Universe. They have shown that “the topology of the Universe can impose significant restrictions upon the type of anisotropies it can sustain”. We will not consider topology in this work but these results are really interesting from the point of view of relations between dynamics and topology which has also been examined by Ashtekar and Samuel[@AshSam91].

The plane of the paper is the following. The second 