A characterization of subshifts with bounded powers
Combinatorics
2011-11-08 v1 Dynamical Systems
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.
Cite
@article{arxiv.1111.1609,
title = {A characterization of subshifts with bounded powers},
author = {Johannes Kellendonk and Daniel Lenz and Jean Savinien},
journal= {arXiv preprint arXiv:1111.1609},
year = {2011}
}
Comments
20 pages, 1 figure