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 Ivashchuk V. V., Melnikov V. N. Billiard Reprezentation for Pseudo-Euclidean Toda-Like Systems of Cosmological Origin 1996, vol. 1, no. 2, pp.  23-35 Abstract The 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. Citation: Ivashchuk V. V., Melnikov V. N.,  Billiard Reprezentation for Pseudo-Euclidean Toda-Like Systems of Cosmological Origin, Regular and Chaotic Dynamics, 1996, vol. 1, no. 2, pp. 23-35 DOI:10.1070/RD1996v001n02ABEH000012