String attractors are a combinatorial tool coming from the field of data compression. It is a set of positions within a word which intersects an occurrence of every factor. While one-sided infinite words admitting a finite string attractor are eventually periodic, the situation is different for two-sided infinite words. In this paper, we characterise the bi-infinite words admitting a finite string attractor as the characteristic Sturmian words and their morphic images. For words that do not admit finite string attractors, we study the structure and properties of their infinite string attractors.

翻译：字符串吸引子是数据压缩领域引入的一种组合工具。它是指词中的一组位置，该位置集合与每个因子的某次出现相交。对于具有有限字符串吸引子的单侧无限词，它们最终是周期性的，但对于双侧无限词，情况则不同。本文中，我们将允许有限字符串吸引子的双向无限词刻画为特征Sturmian词及其形态像。对于不允许有限字符串吸引子的词，我们研究了其无限字符串吸引子的结构与性质。