标题： 奇异点附近的多维宇宙学中相交p膜的台球表示 显示英文标题

标题： Billiard Representation for Multidimensional Cosmology with Intersecting p-branes near the Singularity

摘要： 考虑了一个描述n个爱因斯坦空间在具有l个标量场和形式的理论中的宇宙演化的多维模型。当采用电磁复合p膜假设，并对模型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)维洛巴切夫斯基空间上的弹道运动，N = n+l。使用了弹道体积有限性和紧致性的几何准则。该准则将问题转化为(N-2)维球面由点源照射的问题。考虑了一些弹道体积有限的例子，因此在奇点附近表现出振荡行为。其中包括二维弹道如正方形和三角形（例如Bianchi-IX模型的弹道）以及“截断”的D=11超引力模型中的四维弹道（不包含陈-西蒙斯项）。结果表明，包含陈-西蒙斯项会破坏弹道的限制性。 显示英文摘要

摘要： Multidimensional model describing the cosmological evolution of n Einstein spaces in the theory with l scalar fields and forms is considered. When electro-magnetic composite p-brane ansatz is adopted, and 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, N = n+l. The geometrical criterion for the finiteness of the billiard volume and its compactness is used. This criterion reduces the problem to the problem of illumination of (N-2)-dimensional sphere by point-like sources. Some examples with billiards of finite volume and hence oscillating behaviour near the singularity are considered. Among them examples with square and triangle 2-dimensional billiards (e.g. that of the Bianchi-IX model) and a 4-dimensional billiard in ``truncated'' D = 11 supergravity model (without the Chern-Simons term) are considered. It is shown that the inclusion of the Chern-Simons term destroys the confining of a billiard.