论文标题
有限类型转移的二元因素
Binary factors of shifts of finite type
论文作者
论文摘要
我们构建了两个新的拓扑动力系统；一个是有限类型的单方面移位的因素，而第二个是两侧移位的因素。数据是一个有限的图表，它显示有限类型的偏移，第二个有限的有向图和一对嵌入到第一个的嵌入，满足了某些条件。然后，基于实数的二进制扩展，从一个简单的想法中获得了该因素。在这两种情况下，我们都在因素上构建自然指标，在第二种情况下，从鲁尔尔（Ruelle）的意义上讲，这使该系统成为薄弱的空间。我们计算了这些系统的各种代数不变式，包括作者开发的Smale空间的同源性以及与它们相关的各种$ C^{*} $的K-They-kheory，以与它们相关的代数。
We construct two new classes of topological dynamical systems; one is a factor of a one-sided shift of finite type while the second is a factor of the two-sided shift. The data is a finite graph which presents the shift of finite type, a second finite directed graph and a pair of embeddings of it into the first, satisfying certain conditions. The factor is then obtained from a simple idea based on binary expansion of real numbers. In both cases, we construct natural metrics on the factors and, in the second case, this makes the system a Smale space, in the sense of Ruelle. We compute various algebraic invariants for these systems, including the homology for Smale space developed by the author and the K-theory of various $C^{*}$-algebras associated to them, in terms of the pair of original graphs.
