A classification of aperiodic order via spectral metrics and Jarník sets

Maik Gröger, Marc Kesseböhmer, Arne Mosbach, Tony Samuel, Malte Steffens

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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 languageEnglish
Pages (from-to)3031–3065
Number of pages35
JournalErgodic Theory and Dynamical Systems
Issue number11
Early online date13 Mar 2018
Publication statusPublished - Nov 2019


  • Jarnik sets
  • Spectral metrics
  • Aperiodic order
  • Sturmian words
  • Complexity
  • Continued fractions

ASJC Scopus subject areas

  • Applied Mathematics
  • General Mathematics


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