Billiard representation for pseudo-Euclidean Toda-like systems of cosmological origin

Details Billiard representation for pseudo-Euclidean Toda-like systems of cosmological origin Billiard representation for pseudo-Euclidean Toda-like systems of cosmological origin

2008-11-03

arxiv.org/abs/0811.0283v1

Regular & Chaotic Dynamics, 1, No 2, 23-35 (1996)

Physics

Mathematical Physics

14 pages, PDFLatex, 4 figures (PDF)

Scientific paper

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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