The return sequence of the Bowen–Series map for punctured surfaces
The return sequence of the Bowen–Series map for punctured surfaces
复制标题
穿孔表面的 Bowen 系列图的返回序列
DOI：
10.4064/fm182-3-3
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发表时间：
2004
影响因子：
0.6
通讯作者：
M. Stadlbauer
中科院分区：
文献类型：
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作者：
M. Stadlbauer
对于有限面积的非紧双曲曲面M，研究了测地线流的Poincare截面。第一个返回映射的正则不可逆因子是逐点对偶遍历的，返回序列（an）由an = π 4（Area（M）+ 2π）·nlog（n）给出。我们使用这个结果来推断，部分地图本身是合理的遍历，并与M的测地线流是遍历关于刘维测度。
For a non–compact hyperbolic surface M of finite area, we study a certain Poincare section for the geodesic flow. The canonical, non–invertible factor of the first return map to this section is shown to be pointwise dual ergodic with return sequence (an) given by an = π 4(Area(M) + 2π) · n log(n) . We use this result to deduce that the section map itself is rationally ergodic, and that the geodesic flow associated to M is ergodic with respect to the Liouville measure.