论文标题
极端参数及其二元组图
Extremal parameters and their duals for Fuchsian boundary maps
论文作者
论文摘要
我们使用广义的Bowen系列边界图及其与无共同扭转的无扭转的紫红色群相关的自然扩展描述了恒定负曲率表面上的地球表面上的算术横截面。如果边界图参数是极端的，也就是说，每个都会扩展基本多边形的一侧的大地测量端点，则自然扩展图具有具有有限矩形结构的域，并且相关的算术横截面被此集合参数化。这种结构使我们能够将大地测量流作为符号序列系统上的特殊流程。此外，每个极端参数都有相应的双参数选择，因此，测量算术代码的“过去”是使用双参数的代码的“未来”。 Adler和Flatto观察到了两个经典参数选择的双重性。在这里，我们建设性地表明，每个极端参数集都有偶。
We describe arithmetic cross-sections for geodesic flow on compact surfaces of constant negative curvature using generalized Bowen-Series boundary maps and their natural extensions associated to cocompact torsion-free Fuchsian groups. If the boundary map parameters are extremal, that is, each is an endpoint of a geodesic that extends a side of the fundamental polygon, then the natural extension map has a domain with finite rectangular structure, and the associated arithmetic cross-section is parametrized by this set. This construction allows us to represent the geodesic flow as a special flow over a symbolic system of coding sequences. Moreover, each extremal parameter has a corresponding dual parameter choice such that the "past" of the arithmetic code of a geodesic is the "future" for the code using the dual parameter. This duality was observed for two classical parameter choices by Adler and Flatto; here we show constructively that every extremal parameter set has a dual.
