##### A characterization of subshifts with bounded powers

Review articleOpen access###### J. Kellendonk - No affiliation found

**2013/12/28**DOI: 10.1016/j.disc.2013.08.026

*Full-length article***Journal:**Discrete Mathematics

##### Abstract:

AbstractWe 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.

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