标题： 线性流形上的平移棱柱 显示英文标题

标题： Linear Flows on Translation Prisms

摘要： 受多面体中弹子球研究的启发，我们研究了一类奇异平坦的$3$-流形上的线性流，我们将这些流形称为平移棱柱。 利用Furstenberg和Veech的思想，我们将关于平移曲面上流的弱混合性质的结果与平移棱柱上线性流的遍历性质联系起来，并用此得到有关这些棱柱流和相关弹子球流的独特遍历性的若干结果。 此外，我们构造了伪Anosov方向上具有Pisot展开因子的平移流的显式特征函数，并利用这一构造来构建平移棱柱上非遍历流的显式例子，以及正则$n$-边形上的右棱柱中非遍历弹子球流的例子，其中$n=7, 9, 14, 16, 18, 20, 24, 30$。 显示英文摘要

摘要： Motivated by the study of billiards in polyhedra, we study linear flows in a family of singular flat $3$-manifolds which we call translation prisms. Using ideas of Furstenberg and Veech, we connect results about weak mixing properties of flows on translation surfaces to ergodic properties of linear flows on translation prisms, and use this to obtain several results about unique ergodicity of these prism flows and related billiard flows. Furthermore, we construct explicit eigenfunctions for translation flows in pseudo-Anosov directions with Pisot expansion factors, and use this construction to build explicit examples of non-ergodic prism flows, and non-ergodic billiard flows in a right prism over a regular $n$-gons for $n=7, 9, 14, 16, 18, 20, 24, 30$.