论文标题
Markov分区的恒定负曲率的紧凑riemann表面上的测量流量分区
Markov partitions for the geodesic flow on compact Riemann surfaces of constant negative curvature
论文作者
论文摘要
众所周知，双曲线流允许任意尺寸的马尔可夫分区。但是，马尔可夫分区的一般双曲线流的构造非常抽象，并且不容易理解。为了建立对马尔可夫分区的更详细的理解，在本文中，我们考虑了恒定负曲率的Riemann表面上的地球流量。我们为马尔可夫分区提供了严格的构造，该分区的双曲线流具有明确形式的矩形和局部横截面。还详细计算了本地产品结构。
It is well-known that hyperbolic flows admit Markov partitions of arbitrarily small size. However, the constructions of Markov partitions for general hyperbolic flows are very abstract and not easy to understand. To establish a more detailed understanding of Markov partitions, in this paper we consider the geodesic flow on Riemann surfaces of constant negative curvature. We provide a rigorous construction of Markov partitions for this hyperbolic flow with explicit forms of rectangles and local cross sections. The local product structure is also calculated in detail.
