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1 results

  • Equicontinuous Delone Dynamical Systems

  • Johannes Kellendonk, Daniel Lenz
  • Journal:
    Canadian Journal of Mathematics / Volume 65 / Issue 1 / 01 February 2013
    Published online by Cambridge University Press:
    20 November 2018, pp. 149-170
    Print publication:
    01 February 2013
    • Article
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  • We characterize equicontinuous Delone dynamical systems as those coming from Delone sets with strongly almost periodic Dirac combs. Within the class of systems with finite local complexity, the only equicontinuous systems are then shown to be the crystallographic ones. On the other hand, within the class without finite local complexity, we exhibit examples of equicontinuous minimal Delone dynamical systems that are not crystallographic. Our results solve the problem posed by Lagarias as to whether a Delone set whose Dirac comb is strongly almost periodic must be crystallographic.