论文标题
同步动态系统：换档空间和$ K $ - 理论
Synchronizing Dynamical Systems: Shift Spaces and $K$-Theory
论文作者
论文摘要
在我们以前的工作的基础上，我们对在同步移动空间的特殊情况下开发了用于同步动力系统的技术。在汤姆森（Thomsen）的工作之后，我们为同步的杂智性和同步杂斜利$ c^\ ast $ algebras提供了同步的构造，以及在bratteli图方面的同步偏移空间的理想。详细讨论了我们先前工作（同步理想和同步杂斜代数）中引入的代数。在Sofic Shift案例中，这些代数被证明与其最小左和最小右介绍的$ c^\ ast $ - 代数有关。讨论了几个特定的例子以证明这些技术。对于偶数转变，我们对所有相关不变的完整计算。我们讨论了这些代数的sofic偏移，几乎没有有限的类型和许多严格的非索非同步偏移。特别是，我们讨论了$ k $ - 换档空间的同层代数及其同步理想及其含义的等级。我们还提供了从任何最小移动的生产的构造，一个同步移动偏移的一组非同步点正是原始的最小移位。
Building on our previous work, we give a thorough presentation of the techniques developed for synchronizing dynamical systems in the special case of synchronizing shift spaces. Following work of Thomsen, we give a construction of the homoclinic, the heteroclinic, and synchronizing heteroclinic $C^\ast$-algebras along with the synchronizing ideal of a shift space in terms of Bratteli diagrams. The algebras introduced in our previous work (the synchronizing ideal, and synchronizing heteroclinic algebra) are discussed in detail. In the sofic shift case, these algebras are shown to be related to the $C^\ast$-algebras of its minimal left and minimal right presentations. Several specific examples are discussed to demonstrate these techniques. For the even shift we give a complete computation of all the associated invariants. We discuss these algebras for a sofic shift that is not of almost finite type and for a number of strictly non-sofic synchronizing shifts. In particular we discuss the rank of the $K$-theory of the homoclinic algebra of a shift space and its synchronizing ideal and its implications. We also give a construction for producing from any minimal shift a synchronizing shift whose set of non-synchronizing points is exactly the original minimal shift.
