格空间上horocycle流的Poincaré截面
动力系统
2012-07-24 v2 几何拓扑
数论
摘要
我们构造了模曲面上horocycle流的Poincaré截面，并研究了相关的首次返回映射，该映射与Boca-Cobeli-Zaharescu定义的变换（BCZ映射）一致。我们分类了该映射的遍历不变测度，并证明了周期轨道的等分布。作为推论，我们得到了关于尖点游走平均深度以及Farey序列和格向量斜率间隙分布的结果。
引用
@article{arxiv.1206.6597,
title = {A Poincar\'e section for horocycle flow on the space of lattices},
author = {Jayadev S. Athreya and Yitwah Cheung},
journal= {arXiv preprint arXiv:1206.6597},
year = {2012}
}
备注
39 pages, 12 figures, some updates and added references. The large figure on page 3 has been changed to be more manageable. Submitted to Inventiones Mathematicae