have been studied in [@Jantzen; @Leblanc; @Weaver].

-   The case of the gravity-dilaton-$p$-form system is more complicated to discuss because its behaviour depends on a combination of several factors, namely the dimension $D$, the menu of $p$-forms, and the numerical values of the dilaton couplings. For a given $D$ and a given menu of $p$-forms there exists a “subcritical” domain $\cal D$ (an open neighbourhood of the origin $\lambda_j = 0$ for all $j$’s) such that: (i) when the $\lambda_j$ belong to $\cal D$ the general behaviour is Kasner-like, but (ii) when the $\lambda_j$ do not belong to $\cal D$ the behaviour is oscillatory. Note that $\cal D$ is open. Indeed, the behaviour is oscillatory when the $\lambda_j$ are on the boundary of $\cal D$, as happens for instance for the low-energy bosonic sectors of type I or heterotic superstrings [@dh1]. For a single $p$-form, the subcritical domain $\cal D$ takes the simple form $\vert \lambda_j \vert <\lambda_j^c$, where $\lambda_j^c$ depends on the form-degree and the spacetime dimension. ($\lambda_j^c$ can be infinite.) For a collection of $p$-forms, $\cal D$ is more complicated and not just given by the Cartesian product of the subcritical intervals associated with each individual $p$-form.

The 