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arXiv · 1111.1609

A characterization of subshifts with bounded powers

Johannes Kellendonk·Daniel Lenz·Jean Savinien
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Abstract

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.

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Johannes Kellendonk, Daniel Lenz, Jean Savinien. 2011-11-07. A characterization of subshifts with bounded powers. https://arxiv.org/abs/1111.1609

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