RUSSIAN GRAVITATIONAL ASSOCIATION CENTER FOR SURFACE AND VACUUM RESEARCH DEPARTMENT OF FUNDAMENTAL INTERACTIONS AND METROLOGY RGA-CSVR-012/94 gr-qc/9408004 Dynamics of inhomogeneities of metric in the vicinity of a singularity in multidimensional cosmology

The problem of construction of a general ihomogeneous solution of D-dimensional Einstein equations with any matter sources satisfying the inequality ǫ ≥ p in the vicinity of a cosmological singularity is considered. It is shown that near the singularity a local behavior of metric functions is described by a billiard on a space of a constant negative curvature. The billiard is shown to have a finite volume and consequently to be a mixing one. Dynamics of inhomogeneities of metric is studied and it is shown that its statistical properties admit a complete description. An invariant measure describing statistics of inhomogeneities is obtained and a role of a minimally-coupled scalar field in dynamics of the inhomogeneities is also considered.