Vitaly Melnikov

Moscow, 117334, Andreevskaya nab.,2
Centre for Gravitation and Fundamental Metrology, VNIIMS and Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia


Ivashchuk V. V., Melnikov V. N.
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

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