Spectral Properties of Schrödinger Operators Associated with Almost Minimal Substitution Systems

  title={Spectral Properties of Schr{\"o}dinger Operators Associated with Almost Minimal Substitution Systems},
  author={Benjamin Eichinger and Philipp Gohlke},
  journal={Annales Henri Poincare},
  pages={1377 - 1427}
We study the spectral properties of ergodic Schrödinger operators that are associated with a certain family of non-primitive substitutions on a binary alphabet. The corresponding subshifts provide examples of dynamical systems that go beyond minimality, unique ergodicity and linear complexity. In some parameter region, we are naturally in the setting of an infinite ergodic measure. The almost sure spectrum is singular and contains an interval. We show that under certain conditions, eigenvalues… 
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