  Compactification can control chaotic Mixmaster behavior in gravitational
systems with p-form matter: we consider this in light of the connection between
supergravity models and Kac-Moody algebras. We show that different
compactifications define "mutations" of the algebras associated with the
noncompact theories. We list the algebras obtained in this way, and find novel
examples of wall systems determined by Lorentzian (but not hyperbolic)
algebras. Cosmological models with a smooth pre-big bang phase require that
chaos is absent: we show that compactification alone cannot eliminate chaos in
the simplest compactifications of the heterotic string on a Calabi-Yau, or M
theory on a manifold of G_2 holonomy.
