Article
J. Mod. Dyn. 3:2, 253-270 (2009)
[DOI: 10.3934/jmd.2009.3.253]
Schrödinger Operators defined by Interval Exchange Transformations
Jon Chaika, David Damanik, and Helge Krüger
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 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.
MSC2000: Primary 81Q10; Secondary 37A05, 47B36, 82B44
Keywords: Ergodic Schrödinger operators, singular spectrum, continuous spectrum, interval exchange transformations