2011/11/07 by Johannes Kellendonk, Daniel Lenz, Kellendonk, Johannes +3
Computer Science · Mathematics · #47c15 #68R15 #94A55 #Cellular Automata and Applications #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.CO #math.DS #msc:47c15 #msc:68R15 #msc:94A55
paper · pdf · doi:10.48550/arxiv.1111.1609
20 pages, 1 figure
arxiv created 2011/11/07 · openalex publication_date 2011/11/07 · arxiv updated 2011/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.