Billiard representation for multidimensional cosmology with intersecting p-branes near the singularity

Multidimensional model describing the cosmological evolution of n Einstein spaces in the theory with l scalar fields and forms is considered. When ele ctromagnetic composite p-brane ansatz is adopted, and certain restrictions on the parameters of the model are imposed, the dynamics of the model near the singularity is reduced to a billiard on the (N - 1)-dimensional Lobache vsky space HN-1, N = n + l. The geometrical criterion for the finiteness of the billiard volume and its compactness is used. This criterion reduces th e problem to the problem of illumination of (N - 2)-dimensional sphere SN-2 by pointlike sources. Some examples with billiards of finite volume and he nce oscillating behavior near the singularity are considered. Among them ex amples with square and triangle two-dimensional billiards (e.g., that of th e Bianchi-IX model) and a four-dimensional billiard in "truncated" D = 11 s upergravity model (without the Chern-Simons term) are considered. It is sho wn that the inclusion of the Chern-Simons term destroys the confining of a billiard. (C) 2000 American Institute of Physics. [S0022-2488(00)04808-8].