Constant length substitutions, iterated function systems and amorphic complexity
Constant length substitutions, iterated function systems and amorphic complexity
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DOI：
10.1007/s00209-019-02426-2
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发表时间：
2018-12
影响因子：
0.8
通讯作者：
G. Fuhrmann;M. Gröger
中科院分区：
文献类型：
--
作者：
G. Fuhrmann;M. Gröger
我们展示了如何从分形维数和迭代函数系统的一般理论的几何方法可以部署到零熵制度的符号动力学研究。更确切地说，我们建立了一个维度表征的拓扑概念的无定形复杂性。对于子移位与离散谱相关的恒定长度的替代，这种特性使我们能够推导出边界的无定形的复杂性，通过解释子移位的迭代函数系统的吸引子在一个合适的商空间。其结果是，我们得到了一般的有限性和积极的amorphic复杂性，在这种设置，并提供了一个封闭的公式的情况下，一个二进制字母。
We show how geometric methods from the general theory of fractal dimensions and iterated function systems can be deployed to study symbolic dynamics in the zero entropy regime. More precisely, we establish a dimensional characterization of the topological notion of amorphic complexity. For subshifts with discrete spectrum associated to constant length substitutions, this characterization allows us to derive bounds for the amorphic complexity by interpreting the subshift as the attractor of an iterated function system in a suitable quotient space. As a result, we obtain the general finiteness and positivity of amorphic complexity in this setting and provide a closed formula in case of a binary alphabet.