Symmetric band complexes of thin type and chaotic sections which are not quite chaotic
Symmetric band complexes of thin type and chaotic sections which are not quite chaotic
复制标题
薄型对称带复合体和不太混沌的混沌截面
DOI：
--
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
A. Skripchenko
中科院分区：
文献类型：
--
作者：
I. Dynnikov;A. Skripchenko
在最近的一篇论文中，我们构造了一个薄型叶状2-配合物族，其典型叶具有两个拓扑末端。这里我们给出这样的复合体的更简单的例子，另外，它们是对合对称的，并且具有最小的秩。这允许在三维空间中构造一个具有平面方向的三周期曲面，使得曲面具有中心对称性，并且所选方向的平面部分是混沌的，并且由无限多个连接的组件组成。此外，截面的典型连通分量具有渐近方向，这是由于3环面表面上相应的叶理不是唯一遍历的。
In a recent paper we constructed a family of foliated 2-complexes of thin type whose typical leaves have two topological ends. Here we present simpler examples of such complexes that are, in addition, symmetric with respect to an involution and have the smallest possible rank. This allows for constructing a 3-periodic surface in the three-space with a plane direction such that the surface has a central symmetry, and the plane sections of the chosen direction are chaotic and consist of infinitely many connected components. Moreover, typical connected components of the sections have an asymptotic direction, which is due to the fact that the corresponding foliation on the surface in the 3-torus is not uniquely ergodic.