论文标题
拓扑动态的渐近性和扩张性的几何框架
A geometric framework for asymptoticity and expansivity in topological dynamics
论文作者
论文摘要
我们开发了一个几何框架，以解决拓扑动力学中的渐近性和非跨性。当代理组是第二个可计数且局部紧凑时，我们的框架可以应用。作为应用程序，我们在这种情况下显示了Schwartzman定理的扩展。另外，当代理组为$ {\ mathbb z}^d $时，我们将获得新的结果：$ {\ mathbb r}^d $的任何半空间都包含一个矢量，从Boyle和Lind的意义上定义了（定向的）非倾向的方向。最后，我们推断远端康托尔系统的刚性特性。
We develop a geometric framework to address asymptoticity and nonexpansivity in topological dynamics. Our framework can be applied when the acting group is second countable and locally compact. As an application, we show extensions of Schwartzman's theorem in this context. Also, we get new results when the acting groups is ${\mathbb Z}^d$: any half-space of ${\mathbb R}^d$ contains a vector defining a (oriented) nonexpansive direction in the sense of Boyle and Lind. Finally, we deduce rigidity properties of distal Cantor systems.
