The Asymptotic Behaviour of Tilted Bianchi type VI${}_0$ Universes

We study the asymptotic behaviour of the Bianchi type VI${}_0$ universes with a tilted $\gamma$-law perfect fluid. The late-time attractors are found for the full 7-dimensional state space and for several interesting invariant subspaces. In particular, it is found that for the particular value of the equation of state parameter, $\gamma =6\mathrm{/}5$, there exists a bifurcation line which signals a transition of stability between a non-tilted equilibrium point to an extremely tilted equilibrium point. The initial singular regime is also discussed and we argue that the initial behaviour is chaotic for $\gamma <2$.