线性重复Delone集的塔式系统
Tower systems for Linearly repetitive Delone sets
摘要：
本文研究了线性重复Delone集，继Bellissard，Benedetti和Gambaudo的工作之后，证明了线性重复Delone集的壳包含一个适当嵌套的盒分解序列（塔系统），该序列具有严格正的和一致有界的（在大小和范数上）转移阵.这推广了Durand关于线性递归符号系统的一个结果。此外，我们应用这个结果给出了一个新的证明的经典估计Lagarias和Pleasants的收敛速率的补丁频率。
英文摘要：
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.
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