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2013
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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:

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

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