论文标题
同步动力系统：它们的群体和$ C^*$ - 代数
Synchronizing Dynamical Systems: their groupoids and $C^*$-algebras
论文作者
论文摘要
汤姆森（Thomsen）在Smale空间案例中的Ruelle和Putnam的作品建立基础，定义了用于扩展的动力学系统的同型和异斜$ C^\ AST $ -Algebras。在本文中，我们定义了一类膨胀的动力系统，称为同步动态系统，这些系统几乎在任何地方都表现出双曲线行为。同步动态系统概括了Smale空间（甚至有限呈现的系统）。然而，它们仍然具有理想的动力学特性，例如具有密集的周期点。我们研究了与同步动力学系统相关的各种$ c^\ ast $ - 代数。除其他结果外，我们还表明，同步系统的同层代数包含一个理想，其表现类似于Smale空间的同型代数。
Building on work of Ruelle and Putnam in the Smale space case, Thomsen defined the homoclinic and heteroclinic $C^\ast$-algebras for an expansive dynamical system. In this paper we define a class of expansive dynamical systems, called synchronizing dynamical systems, that exhibit hyperbolic behavior almost everywhere. Synchronizing dynamical systems generalize Smale spaces (and even finitely presented systems). Yet they still have desirable dynamical properties such as having a dense set of periodic points. We study various $C^\ast$-algebras associated with a synchronizing dynamical system. Among other results, we show that the homoclinic algebra of a synchronizing system contains an ideal which behaves like the homoclinic algebra of a Smale space.
