Tower systems for linearly repetitive Delone sets
Tower systems for linearly repetitive Delone sets
复制标题
用于线性重复 Delone 装置的塔式系统
DOI：
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发表时间：
2010
影响因子：
0.9
通讯作者：
D. Coronel
中科院分区：
文献类型：
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作者：
José Aliste;D. Coronel
本文研究了线性重复Delone集，并在Bellissard，Benedeti和Gambaudo的工作基础上证明了线性重复Delone集的壳容许盒分解(塔系)的适当嵌套序列具有严格正的且一致有界(大小和范数)的转移矩阵。这推广了Durand关于线性循环符号系统的一个结果。此外，我们应用这一结果给出了Lagarias和Pleasants关于斑块频率收敛速度的经典估计的一个新的证明。
Abstract In this paper we study linearly repetitive Delone sets and prove, following the work of Bellissard, Benedetti and Gambaudo, that the hull of a linearly repetitive Delone set admits a properly nested sequence of box decompositions (tower system) with strictly positive and uniformly bounded (in size and norm) transition matrices. This generalizes a result of Durand for linearly recurrent symbolic systems. Furthermore, we apply this result to give a new proof of a classic estimation of Lagarias and Pleasants on the rate of convergence of patch frequencies.