论文标题
对单孔扩张托里动力学的完整研究
A Full Study of the Dynamics on One-Holed Dilation Tori
论文作者
论文摘要
扩张表面研究中的一个空旷的问题是确定固定扩张表面方向流的典型动力学行为。我们表明，在任何一个单孔的扩张圆环上，除了尺寸零第托方向外，方向流具有吸引周期性轨道，或完全周期性。我们进一步表明，对于此第托集中的方向，将方向流动吸引到鞍形连接或表面上的层压板，这是局部度量的零插槽集和间隔的乘积。
An open question in the study of dilation surfaces is to determine the typical dynamical behavior of the directional flow on a fixed dilation surface. We show that on any one-holed dilation torus, in all but a measure zero Cantor set of directions, the directional flow has an attracting periodic orbit, is minimal, or is completely periodic. We further show that for directions in this Cantor set, the directional flow is attracted to either a saddle connection or a lamination on the surface that is locally the product of a measure zero Cantor set and an interval.
