Substitution and Tiling Dynamics: Introduction to Self-inducing Structures - CIRM Jean-Morlet Chair, Fall 2017
Substitution and Tiling Dynamics: Introduction to Self-inducing Structures - CIRM Jean-Morlet Chair, Fall 2017
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替代和平铺动力学：自感应结构简介 - CIRM Jean-Morlet 主席，2017 年秋季
DOI：
10.1007/978-3-030-57666-0_7
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Baake M
中科院分区：
文献类型：
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作者：
Baake M
对于可以用投影方法构造的点集和平铺，人们对相关结构以及相应的光谱有很好的理解，无论是在动力学意义上还是在衍射意义上。对于由替代或膨胀规则定义的系统，情况就不那么有利了，特别是在研究得很多的皮索替代类之外。在这方面的贡献，几何通货膨胀规则访问的自相似和自仿射通货膨胀平铺和它们的傅里叶变换的精确重整化关系的装置的对相关措施。特别是，我们期待到足够的标准，绝对连续的光谱贡献的情况下，并说明了这一点，从类块替换的例子。我们还讨论了Frank-Robinson平铺，作为一个平面的例子，具有无限的局部复杂性和奇异连续谱。
For point sets and tilings that can be constructed with the projection method, one has a good understanding of the correlation structure, and also of the corresponding spectra, both in the dynamical and in the diffraction sense. For systems defined by substitution or inflation rules, the situation is less favourable, in particular beyond the much-studied class of Pisot substitutions. In this contribution, the geometric inflation rule is employed to access the pair correlation measures of self-similar and self-affine inflation tilings and their Fourier transforms by means of exact renormalisation relations. In particular, we look into sufficient criteria for the absence of absolutely continuous spectral contributions, and illustrate this with examples from the class of block substitutions. We also discuss the Frank–Robinson tiling, as a planar example with infinite local complexity and singular continuous spectrum.