Avoiding cosmological chaos with S-branes

In 4 dimensions there are cosmological models which exhibit chaotic BKL oscillations as one approaches the initial singularity i.e. the Kasner parameters \oscillate " between dierent values as ! +0. Similar BKL oscillations have been found in higher dimensional, string inspired cosmological models, which have form elds and scalar dilaton elds, and it has been conjectured that this behavior is generic in such higher dimensional cosmologies. In this essay we give an example where this chaotic behavior is avoided. The system is 5 dimensional spacetime with 3-form elds; the metric is diagonal and the form eld describes a \maximal " set of composite, electric S-branes. When the composite S-branes are replaced by non-composite S-branes chaotic oscillation occur again. This leads us to propose the conjecture that the occurrence or non-occurrence of chaotic oscillating behavior for diagonal metrics depends on the character of the S-brane { composite or non-composite. In [1] Belinskii, Lifshitz and Khalatnikov investigated the dynamics of 4-dimensional Bianchi-IX cosmological solutions. They found that near the initial singularity these solutions took a Kasner form but with the Kasner parameters performing a never-ending chaotic oscillations a