几乎线性重复Delone集的离散性和可求直性
Discrepancy and rectifiability of almost linearly repetitive Delone sets
摘要：
我们扩展了Lagarias和Pleasants的局部权重分布线性重复Delone集的差异范围，并表明类似的范围也适用于更一般的情况下，Delone集没有有限的局部复杂性，如果线性重复取代$\varepsilon$ -线性重复。因此，我们建立的Delone集是$\varepsilon$ -线性重复的一些足够小的$\varepsilon$是可校正的，和不可分割的多尺度替代平铺从来没有几乎线性重复。
英文摘要：
We extend a discrepancy bound of Lagarias and Pleasants for local weight distributions on linearly repetitive Delone sets and show that a similar bound holds also for the more general case of Delone sets without finite local complexity if linear repetitivity is replaced by $\varepsilon$-linear repetitivity. As a result we establish that Delone sets that are $\varepsilon$-linear repetitive for some sufficiently small $\varepsilon$ are rectifiable, and that incommensurable multiscale substitution tilings are never almost linearly repetitive.
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