A characterization of subshifts with bounded powers
A characterization of subshifts with bounded powers
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具有有限功率的子换档的表征
DOI：
10.1016/j.disc.2013.08.026
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
J. Savinien
中科院分区：
文献类型：
--
作者：
Johannes Kellendonk;Daniel Lenz;J. Savinien
我们考虑极小的非周期符号子移位，并证明了如何利用度量性质刻画有界幂的组合性质。为此，我们构造了一族都逼近于子移位空间的图族，并在每个图上定义了一个度量，它推广到子移位空间上的度量。然后，通过适当定义的下确界度量与相应的上确界度量的Lipschitz等价，给出了有界幂的特征。我们还引入了Zeta-函数，并将它们的收敛横坐标与子移位的各种复杂性指数联系起来。我们的结果是基于非对易几何中的结构的，这是两位作者先前工作的结果。
We consider minimal, aperiodic symbolic subshifts and show how to characterize the combinatorial property of bounded powers by means of a metric property. For this purpose we construct a family of graphs which all approximate the subshift space, and define a metric on each graph, which extends to a metric on the subshift space. The characterization of bounded powers is then given by the Lipschitz equivalence of a suitably defined infimum metric with the corresponding supremum metric. We also introduce zeta-functions and relate their abscissa of convergence to various exponents of complexity of the subshift. Our results, following a previous work of two of the authors, are based on constructions in non commutative geometry.