标题： 通过归一化方法研究非周期性膨胀规则的对相关性：一些有趣的例子 显示英文标题

标题： Pair correlations of aperiodic inflation rules via renormalisation: Some interesting examples

摘要： 本文以一种说明性的方式，提出了对常长度替换谱理论扩展的第一步。 我们的出发点是普遍观察到的符号图景（由替换规则定义）及其几何对应物（由诱导的膨胀规则定义的自然原型尺寸）可能有很大差异。 在几何方面，一个非周期性膨胀系统对其对相关系数具有精确的归一化关系。 在这里，我们为一些典型的例子推导出这些关系，并推断出各种谱后果。 特别是，我们考虑斐波那契链，重新审视Thue--Morse和Rudin--Shapiro系统，最后分析了一个具有混合奇异谱的银比例链的扭曲扩展。 显示英文摘要

摘要： This article presents, in an illustrative fashion, a first step towards an extension of the spectral theory of constant length substitutions. Our starting point is the general observation that the symbolic picture (as defined by the substitution rule) and its geometric counterpart with natural prototile sizes (as defined by the induced inflation rule) may differ considerably. On the geometric side, an aperiodic inflation system possesses a set of exact renormalisation relations for its pair correlation coefficients. Here, we derive these relations for some paradigmatic examples and infer various spectral consequences. In particular, we consider the Fibonacci chain, revisit the Thue--Morse and the Rudin--Shapiro sytem, and finally analyse a twisted extension of the silver mean chain with mixed singular spectrum.