On the billiard approach in multidimensional cosmological models

A short overview of the billiard approach for cosmological-type models with n Einstein factor spaces is presented. We start with the billiard representation for pseudo-Euclidean Toda-like systems of cosmological origin. Then we consider cosmological models with a multicomponent perfect-fluid and with composite branes. The second case describes cosmological and spherically symmetric configurations in a theory with scalar fields and fields of forms. The conditions for appearance of asymptotic Kasnerlike and oscillating behaviors in the limits τ → +0 and τ → +∞ (where τ is the synchronous variable) are formulated (e.g., in terms of inequalities for Kasner parameters). Examples of billiards related to the hyperbolic Kac-Moody algebras E 10, AE 3 and A 1,II are given. © 2009 Pleiades Publishing, Ltd.