2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173133The pseudo-Euclidean Toda-like system of cosmological origin is considered. When 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 Lobachevsky space H^{n-1}. The geometrical criterion for the finiteness of the billiard volume and its compactness is suggested. This criterion reduces the problem to the problem of illumination of (n-2)-dimensional sphere S^{n-2} by point-like sources. Some examples are considered.14 pages, PDFLatex, 4 figures (PDF)Mathematical PhysicsGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theorytext