A classification of aperiodic order via spectral metrics and Jarn\'ik sets
| Autor: | Malte Steffens, Arne Mosbach, Marc Kesseböhmer, Tony Samuel, Maik Gröger |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Applied Mathematics
General Mathematics 010102 general mathematics 0102 computer and information sciences 52C23 68R15 94A55 47C15 11K60 37C45 11J70 46L87 01 natural sciences 010201 computation theory & mathematics Aperiodic graph Order (business) Applied mathematics 0101 mathematics Mathematics - Dynamical Systems Mathematical Physics Mathematics |
| Popis: | Given an $\alpha > 1$ and a $\theta$ with unbounded continued fraction entries, we characterise new relations between Sturmian subshifts with slope $\theta$ with respect to (i) an $\alpha$-H\"oder regularity condition of a spectral metric, (ii) level sets defined in terms of the Diophantine properties of $\theta$, and (iii) complexity notions which we call $\alpha$-repetitive, $\alpha$-repulsive and $\alpha$-finite; generalisations of the properties known as linearly repetitive, repulsive and power free, respectively. We show that the level sets relate naturally to (exact) Jarn\'{\i}k sets and prove that their Hausdorff dimension is $2/(\alpha + 1)$. Comment: 25 pages, 1 figure |
| Databáze: | OpenAIRE |
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