论文标题
关于$ \ MATHCAL {S} $的符号因素 - 有限拓扑等级的ADIC subshifts
On symbolic factors of $\mathcal{S}$-adic subshifts of finite topological rank
论文作者
论文摘要
本文研究了有限字母等级的$ \ Mathcal {s} $的符号因素的几个方面。首先，我们解决了[DDPM20]中提出的一个问题，即$ \ MATHCAL {S} $ - ADIC subshifts的象征性因素的拓扑等级，并证明该排名最多是扩展系统之一，从[E20]和[GH2020]中提高了结果。由于我们的方法，我们证明有限的拓扑等级系统是合并的。其次，我们研究了因子$π^{ - 1}（y）$的结构。最后，我们证明有限拓扑等级的固定子缩影的符号因子（直至结合）的数量是有限的，因此扩展了Durand在线性反复的子缩影上的相似定理。
This paper studies several aspects of symbolic factors of $\mathcal{S}$-adic subshifts of finite alphabet rank. First, we address a problem raised in [DDPM20] about the topological rank of symbolic factors of $\mathcal{S}$-adic subshifts and prove that this rank is at most the one of the extension system, improving results from [E20] and [GH2020]. As a consequence of our methods, we prove that finite topological rank systems are coalescent. Second, we investigate the structure of fibers $π^{-1}(y)$ of factor maps $π\colon(X,T)\to(Y,T)$ between minimal $\mathcal{S}$-adic subshifts of finite alphabet rank and show that they have the same finite cardinality for all $y$ in a residual subset of $Y$. Finally, we prove that the number of symbolic factors (up to conjugacy) of a fixed subshift of finite topological rank is finite, thus extending Durand's similar theorem on linearly recurrent subshifts.
