Abstract

Let $b\ge 2$ be an integer. Using Sturmian words we describe all irrational real numbers $\xi$ such that the image in $ℝ∕\mathbb{Z}$ of the sequence ${(\xi {(-b)}^n)}_{n\ge 0}$ is contained in an interval of length $b^{-1}+b^{-2}-b^{-3}$. In previous work we showed that the image cannot be contained in a shorter interval.

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