论文标题
$ g $索引，拓扑动力和标记属性
$G$-index, topological dynamics and marker property
论文作者
论文摘要
鉴于有限的$ g $的行动，我们可以定义其指数。 $ g $索引大致测量给定的$ g $空间的大小。我们探索$ g $索引理论与拓扑动态之间的联系。对于定点的免费动力学系统，我们研究了$ p $ - 周期点的$ \ mathbb {z} _p $ - 索引。我们发现它的增长最多是$ p $的线性。作为一个应用程序，我们构建了一个没有标记属性的自由动力系统。这解决了已经开放了几年的问题。
Given an action of a finite group $G$, we can define its index. The $G$-index roughly measures a size of the given $G$-space. We explore connections between the $G$-index theory and topological dynamics. For a fixed-point free dynamical system, we study the $\mathbb{Z}_p$-index of the set of $p$-periodic points. We find that its growth is at most linear in $p$. As an application, we construct a free dynamical system which does not have the marker property. This solves a problem which has been open for several years.
