论文标题
双曲机上多边形台球的有限性
Finiteness in Polygonal Billiards on Hyperbolic Plane
论文作者
论文摘要
\ textsc {j。 Hadamard}研究了在负曲率表面上测量流的几何特性，从而启动了“符号动力学”。 在本文中，我们遵循相同的几何方法来研究双曲机上“有理多边形”中台球的大地轨迹。我们特别表明，因此产生的台球动态只是“有限类型的亚缩放”或其密集的子集。我们进一步表明，“有限类型的subshifts”在子缩合动力学中起着核心作用，并在讨论所有乘坐空间的拓扑结构时，我们证明了它们近似于任何移动动态。
\textsc{J. Hadamard} studied the geometric properties of geodesic flows on surfaces of negative curvature, thus initiating "Symbolic Dynamics". In this article, we follow the same geometric approach to study the geodesic trajectories of billiards in "rational polygons" on the hyperbolic plane. We particularly show that the billiard dynamics resulting thus are just 'Subshifts of Finite Type' or their dense subsets. We further show that 'Subshifts of Finite Type' play a central role in subshift dynamics and while discussing the topological structure of the space of all subshifts, we demonstrate that they approximate any shift dynamics.
