论文标题
在有限的间隔等单词和subshift上
On finite spacer rank for words and subshifts
论文作者
论文摘要
我们定义了我们称之为间隔等级的单词和子缩短的等级概念，从而扩展了Gao和Hill的排名一号象征性变化的概念。我们构建了每个有限间隔等级的无限单词，无限的间隔等级，并显示存在没有间隔等级构造的单词。我们认为单词是替代点的固定点，并为单词提供了明确的条件，以使最多有两个构造，而不是排名第一。我们证明，有限的间隔等级子缩影的拓扑熵为零，并且零熵子的换档未由具有有限间隔等级构造的单词定义。我们还研究了与无限词相关的转移系统，包括与Sturmian序列相关的移位系统，我们显示的是间隔级别两个系统。
We define a notion of rank for words and subshifts that we call spacer rank, extending the notion of rank-one symbolic shifts of Gao and Hill. We construct infinite words of each finite spacer rank, of unbounded spacer rank, and show there exist words that do not have a spacer rank construction. We consider words that are fixed points of substitutions and give explicit conditions for the word to have an at most spacer rank two construction, and not to be rank one. We prove that finite spacer rank subshifts have topological entropy zero, and that there are zero entropy subshifts not defined by a word with a finite spacer rank construction. We also study shift systems associated with infinite words, including those associated to Sturmian sequences, which we show are spacer rank-two systems.
