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16345 results in Geometry and topology

Page 40 of 818

  • Model sets with Euclidean internal space

  • Part of
  • MAURICIO ALLENDES CERDA, DANIEL CORONEL
  • Journal:
    Ergodic Theory and Dynamical Systems / Volume 43 / Issue 12 / December 2023
    Published online by Cambridge University Press:
    11 January 2023, pp. 3897-3922
    Print publication:
    December 2023
    • Article
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  • We give a characterization of inter-model sets with Euclidean internal space. This characterization is similar to previous results for general inter-model sets obtained independently by Baake, Lenz and Moody, and Aujogue. The new ingredients are two additional conditions. The first condition is on the rank of the abelian group generated by the set of internal differences. The second condition is on a flow on a torus defined via the address map introduced by Lagarias. This flow plays the role of the maximal equicontinuous factor in the previous characterizations.

Page 40 of 818