On the billiard approach in multidimensional cosmological models

V.D. Ivashchuk and V.N. Melnikov1

Abstract

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 Kasner-like and oscillating behaviors in the limits t® +0 and t® +¥ (where t 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 E10, AE3 and A1,II are given.

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