Schrödinger Operators Defined by Interval Exchange Transformations
arXiv:0809.3230 · doi:10.3934/jmd.2009.3.253
Abstract
We discuss discrete one-dimensional Schrödinger operators whose potentials are generated by an invertible ergodic transformation of a compact metric space and a continuous real-valued sampling function. We pay particular attention to the case where the transformation is a minimal interval exchange transformation. Results about the spectrum and the spectral type of these operators are established. In particular, we provide the first examples of transformations for which the associated Schrödinger operators have purely singular spectrum for every non-constant continuous sampling function.