Finite blocking property versus pure periodicity
Finite blocking property versus pure periodicity
复制标题
有限阻塞特性与纯周期性
DOI：
10.1017/s014338570800031x
复制
发表时间：
2004
影响因子：
0.9
通讯作者：
T. Monteil
中科院分区：
文献类型：
--
作者：
T. Monteil
翻译表面？是说有有限的阻塞属性，如果对每一对（O，A）的点？存在有限数量的“阻塞”点B1，.，Bn，使得从O到A的每个测地线满足B1之一。?如果定向流在其定向流包含周期性轨迹的每个方向上都是周期性的，则称为纯周期性的（这意味着？允许在这些方向上的圆柱体分解）。我们将证明有限阻塞性质蕴含纯周期性。我们还将具有有限块性质的曲面分类为亏格2：这类曲面就是环面分支覆盖。此外，我们证明了在每一层，这样的表面形成一个集的零测量。在附录A中，我们证明了完全周期平移曲面在每个层中形成一个零测度集。
Abstract A translation surface ? is said to have the finite blocking property if for every pair (O,A) of points in ? there exists a finite number of ‘blocking’ points B1,…,Bn such that every geodesic from O to A meets one of the Bis. ? is said to be purely periodic if the directional flow is periodic in each direction whose directional flow contains a periodic trajectory (this implies that ? admits a cylinder decomposition in such directions). We will prove that the finite blocking property implies pure periodicity. We will also classify the surfaces that have the finite blocking property in genus two: such surfaces are exactly the torus branched coverings. Moreover, we prove that in every stratum such surfaces form a set of null measure. In Appendix A, we prove that completely periodic translation surfaces form a set of null measure in every stratum.