Spectral and arithmetic structures in aperiodic order

  • Michael Baake

    Universität Bielefeld, Germany
  • Franz Gähler

    Universität Bielefeld, Germany
  • Christian Huck

    Universität Bielefeld, Germany
  • Peter Zeiner

    Xiamen University Malaysia, Sepang, Selangor, Malaysia
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Abstract

Systems with aperiodic order can display a variety of arithmetic, combinatorial and spectral phenomena, some of which are reviewed and discussed here. At the same time, the underlying compact tiling spaces can be compared via their topological and spectral invariants. The latter are explicitly computable for substitution systems and provide an important tool for their classification.