larger than the largest amplitude of $6z$ as instance). In this case, the results of the previous sections do not apply since all the variables do not reach equilibrium but an isotropic equilibrium state eventually occurs with $(x_\pm,w)$ only reaching equilibrium. Then, since $\ell$ can be a regular functions as well as having a chaotic behaviour, it is not possible to give more characteristics about it or the way $x_\pm$ would reach equilibrium. Hence, the main result of this subsection is mainly a limitation of the previous subsections results which will be valid for all the Bianchi class A models.\
Let us examine the folowing example for the Bianchi type II model:\
Since $x_\pm$ and $w$ vanish, asymptotically the constraint is $24y^2+12z^2=1$. In this limit, considering that (\[eq4\]) is essentially equivalent to the constraint equation under (\[eq3\]), (\[eq3\]) is the only nontrivial equation. In this asymptotic reduction, (\[eq3\]) can be regarded as the equation for $\ell$ in terms of $y$, which can be written as: $$\ell=\frac{\dot v}{2+v}\frac{1}{\sqrt{1-v}}+\sqrt{1-v},$$ where $v=2(36y^2-1)$ and $6z=\sqrt{1-v}$. For any function for $v(\Omega)$, the equation $$\dot \phi=\frac{12\phi}{\sqrt{3+2\omega}}z,$$ determines $\phi$ as a function of $\Omega$ for a given $\omega$. Then, the definition of $\ell$, $$\ell=\frac{\phi}{\sqrt{3+2\omega}}\frac{U_\phi}{U},$$ determines $U$ as 