形态词与等分布序列
Morphic words and equidistributed sequences
摘要：
我们考虑的问题如下：给定一个有序字母表上的无限单词$w$，构造序列$ν_w=(ν[n])_n$，在$[0,1]$上均匀分布，使得$ν[m]<ν[n]$当且仅当$σ^m(w)<σ^n(w)$，其中$σ$是移位操作，擦除$w$的第一个符号。序列$ν_w$存在，并且对于每个因子具有明确定义的正一致频率的每个字是唯一的，或者，在动力学术语中，对于唯一遍历子移位的每个元素是唯一的。本文描述了当$w$的子移位由一种特殊类型的态射生成时的$ν_w$的构造，并克服了一些技术困难，将结果推广到所有的二元态射.在这种情况下，序列$ν_w$也用态射构造。最后，我们介绍了一个软件工具，它给出了一个二元态射$φ$，计算与$φ$的不动点相关的等分布序列在扩展区间和首元素上的态射。
英文摘要：
The problem we consider is the following: Given an infinite word $w$ on an ordered alphabet, construct the sequence $ν_w=(ν[n])_n$, equidistributed on $[0,1]$ and such that $ν[m]<ν[n]$ if and only if $σ^m(w)<σ^n(w)$, where $σ$ is the shift operation, erasing the first symbol of $w$. The sequence $ν_w$ exists and is unique for every word with well-defined positive uniform frequencies of every factor, or, in dynamical terms, for every element of a uniquely ergodic subshift. In this paper we describe the construction of $ν_w$ for the case when the subshift of $w$ is generated by a morphism of a special kind; then we overcome some technical difficulties to extend the result to all binary morphisms. The sequence $ν_w$ in this case is also constructed with a morphism. At last, we introduce a software tool which, given a binary morphism $φ$, computes the morphism on extended intervals and first elements of the equidistributed sequences associated with fixed points of $φ$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
