String attractors are a combinatorial tool coming from the field of data compression. It is a set of positions within a word which captures 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 article, 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的一种组合工具，它是指单词中的一组位置，能够捕获每个因子的一次出现。虽然存在有限字符串吸引子的单侧无限词是最终周期的，但两侧无限词的情况则不同。本文中，我们将存在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。对于不存在有限字符串吸引子的词，我们研究其无限字符串吸引子的结构与性质。