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Let $X$ be a subshift on a finite alphabet. I'm interested in the following property: there exist words $s,t\in\mathcal L(X)$ (the language of $X$) such that $\{s,t\}^*\subset \mathcal L(X)$. That is, ...

It is a known fact [1] that, for every $c\in (1,\infty]$, it is possible to find a finite alphabet $\mathcal{A}$ and a word $w\in \mathcal{A}^\omega$ such that $w$ has critical exponent $c$. It looks ...