标题： 同步动力系统：有限表示系统和Ruelle代数 显示英文标题

标题： Synchronizing Dynamical Systems: Finitely presented systems and Ruelle algebras

摘要： 本文的主要目标是确定与有限表示系统相关的$C^\ast$-代数的结构，并发展与一般同步系统相关的Ruelle代数的基本理论。后者与前者有关，因为我们证明了与有限表示系统相关的Ruelle代数明确地与Smale空间的情况相关。然而，我们给出了一个sofic移位的例子，其中Ruelle代数不是Poincare对偶（而在Smale空间的情况下，这种对偶性成立）。相关的$C^\ast$-代数是我们在同步系统之前的工作中引入的同步异宿代数。它们与Thomsen之前的工作密切相关，而Thomsen则是建立在Ruelle、Putnam和Spielberg的工作基础上的。 显示英文摘要

摘要： The main goals of the present paper are to determine the structure of the $C^\ast$-algebras associated to a finitely presented system and to develop the basic theory of the Ruelle algebras associated to a general synchronizing system. The later is related to the former in the sense that we show that Ruelle algebras associated to a finitely presented system are explicitly related to the Smale space case. Nevertheless, we give an example of a sofic shift where the Ruelle algebras are not Poincare dual (whereas this duality holds in the Smale space case). The relevant $C^\ast$-algebras are the synchronizing heteroclinic algebras that were introduced in our previous work on synchronizing systems. They are very much related to previous work of Thomsen, who in turn was building on work of Ruelle, Putnam, and Spielberg.