Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647490 | Discrete Mathematics | 2013 | 14 Pages |
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. Our results, following a previous work of two of the authors, are based on constructions in non commutative geometry.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
J. Kellendonk, D. Lenz, J. Savinien,