Dynamical versus diffraction spectrum for structures with finite local complexity
Dynamical versus diffraction spectrum for structures with finite local complexity
复制标题
具有有限局部复杂性的结构的动力学与衍射谱
DOI：
10.1017/etds.2014.28
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发表时间：
2013
影响因子：
0.9
通讯作者：
A. V. van Enter
中科院分区：
文献类型：
--
作者：
M. Baake;D. Lenz;A. V. van Enter
众所周知，遍历测度动力系统的动力学谱与系统中典型元素的衍射测度有关。这种情况包括遍历子移位从符号动力学以及遍历Delone动力系统，都通过适当的嵌入。当谱是纯点时，这种联系就很容易理解了，因为这两个谱的概念在本质上是等价的。然而，一般来说，动力学谱更丰富。在这里，我们认为（唯一）遍历系统的有限的局部复杂性和建立等价的动力学谱的衍射谱的系统和某些因素的集合。这种等效性使得可以通过这些衍射谱来获得动力学谱。它是特别有用的，因为衍射光谱通常更容易确定，在许多情况下，只有很少的需要计算。
It is well known that the dynamical spectrum of an ergodic measure dynamical system is related to the diffraction measure of a typical element of the system. This situation includes ergodic subshifts from symbolic dynamics as well as ergodic Delone dynamical systems, both via suitable embeddings. The connection is rather well understood when the spectrum is pure point, where the two spectral notions are essentially equivalent. In general, however, the dynamical spectrum is richer. Here, we consider (uniquely) ergodic systems of finite local complexity and establish the equivalence of the dynamical spectrum with a collection of diffraction spectra of the system and certain factors. This equivalence gives access to the dynamical spectrum via these diffraction spectra. It is particularly useful as the diffraction spectra are often simpler to determine and, in many cases, only very few of them need to be calculated.