Pisot Substitutions and Exact Regularity

  title={Pisot Substitutions and Exact Regularity},
  author={Marcy Barge and Henk Bruin and Leslie Jones and Lorenzo Sadun},
We consider one-dimensional substitution tiling spaces where the dilatation (stretching factor) is a degree d Pisot number, and the first rational Čech cohomology is d-dimensional. We construct examples of such “homological Pisot” substitutions whose tiling flows do not have pure discrete spectra. These examples are not unimodular, and we conjecture that… CONTINUE READING