Are Kaluza-Klein models of the universe chaotic?

The generic behavior of vacuum inhomogeneous and spatially homogeneous Kaluza-Klein models is studied in the vicinity of the cosmological singularity. It is shown that, in space-time dimensions ≥ 11, the generalized Kasner solution, with monotonic power-law behavior of the spatial distances, becomes a general solution of the Einstein vacuum field equations and that, moreover, the chaotic oscillatory behavior disappears. On the other hand, the chaotic oscillatory behavior, absent in diagonal spatially homogeneous cosmological models in space-time dimensions between 5 and 10, can be reestablished when off-diagonal terms are included.