论文标题
Tori的某些分支封面的马鞍连接方向的间隙
Gaps of saddle connection directions for some branched covers of tori
论文作者
论文摘要
我们计算两类翻译表面的马鞍连接方向的间隙分布。一个类是由沿缝隙粘合两个相同的摩tori的翻译表面。这些产生了非晶格翻译表面的差距分布的第一个明确计算。我们表明，此分布在0和二次尾巴衰减处有支撑。我们还在任何属$ d> 1 $中构建了翻译表面的示例，它们具有与沿裂缝胶合的两个相同托里的间隙分布相同的差距分布。我们考虑的第二类是两次标记的摩托车和鞍座连接，在不同的标记点之间。这些结果可以解释为仿射晶格斜率的间隙分布。我们通过将差距分布的问题转换为一个动态的回报时间问题来获得我们的结果，以在适当的模量空间上的肌肉流动下的横向流程。
We compute the gap distribution of directions of saddle connections for two classes of translation surfaces. One class will be the translation surfaces arising from gluing two identical tori along a slit. These yield the first explicit computations of gap distributions for non-lattice translation surfaces. We show that this distribution has support at 0 and quadratic tail decay. We also construct examples of translation surfaces in any genus $d>1$ that have the same gap distribution as the gap distribution of two identical tori glued along a slit. The second class we consider are twice-marked tori and saddle connections between distinct marked points. These results can be interpreted as the gap distribution of slopes of affine lattices. We obtain our results by translating the question of gap distributions to a dynamical question of return times to a transversal under the horocycle flow on an appropriate moduli space.
