宇宙学起源的类Toda伪欧系统的台球表示
Billiard representation for pseudo-Euclidean Toda-like systems of cosmological origin
摘要：
本文讨论了宇宙学起源的伪欧几里德Toda类系统。当对模型的参数施加某些限制时，模型在"奇点“附近的动力学被简化为（n-1）维罗巴切夫斯基空间H^{n-1}上的台球。提出了台球体积有限的几何判据及其紧致性。该准则将问题简化为（n-2）维球面S^{n-2}被点状源照射的问题。一些例子被认为是。
英文摘要：
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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