are heuristic arguments, supported by numerical study, [@BK2; @DHS2; @Berger00; @BG] that suggest that if one starts with initial data that do not fulfill the inequalities, one ends up, after a finite transient period (with a finite number of “collisions" with potential walls), with a solution that is asymptotically velocity-dominated, for which the inequalities are fulfilled almost everywhere. In that sense, the inequalities would not represent a real restriction since there is a dynamical mechanism that drives the solution to the regime where they are satisfied. For the subcritical values of the dilaton couplings that make the inequalities defining $V$ consistent, there is thus no evidence for an alternative oscillatory regime corresponding to a different (open) region in the space of initial data[^5]. It has indeed been shown that the inequalities defining $V$ are no restriction in a large spatially homogeneous class [@mix]. Such rigorous results are, however, lacking in the inhomogeneous case. In fact, an interesting subtlety might take place in the inhomogeneous case. The heuristic arguments and numerical studies of [@Berger00; @BG] suggest the possibility that the mechanism driving the system to $V$ may be suppressed at exceptional spatial points in general spacetimes, with the result that the 