论文标题
差不多的数字，Kronecker的定理以及Sturmian特征序列的多样性
Badly approximable numbers, Kronecker's theorem, and diversity of Sturmian characteristic sequences
论文作者
论文摘要
在$Nθ$的分数部分中，我们给出了经典的``三范围范围定理''的最佳版本，如果$θ$是一个不可行的数字，那么$nθ$。结果，我们在一个维度中推断出Kronecker的不均匀近似定理的版本，以使数字不佳。我们将这些结果应用于特征性的Sturmian序列的改进序列多样性的量度，在该斜坡上差异很差。
We give an optimal version of the classical ``three-gap theorem'' on the fractional parts of $n θ$, in the case where $θ$ is an irrational number that is badly approximable. As a consequence, we deduce a version of Kronecker's inhomogeneous approximation theorem in one dimension for badly approximable numbers. We apply these results to obtain an improved measure of sequence diversity for characteristic Sturmian sequences, where the slope is badly approximable.
