Abstract
Given an α> and a with unbounded continued fraction entries, we characterize new relations between Sturmian subshifts with slope with respect to (i) an -Hölder regularity condition of a spectral metric, (ii) level sets defined in terms of the Diophantine properties of , and (iii) complexity notions which we call -repetitiveness, -repulsiveness and -finiteness - generalizations of the properties known as linear repetitiveness, repulsiveness and power freeness, respectively. We show that the level sets relate naturally to (exact) Jarník sets and prove that their Hausdorff dimension is 2(α + 1).
Original language | English |
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Pages (from-to) | 3031–3065 |
Number of pages | 35 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 39 |
Issue number | 11 |
Early online date | 13 Mar 2018 |
DOIs | |
Publication status | Published - Nov 2019 |
Keywords
- Jarnik sets
- Spectral metrics
- Aperiodic order
- Sturmian words
- Complexity
- Continued fractions
ASJC Scopus subject areas
- Applied Mathematics
- Mathematics(all)