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
Publications:
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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.
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