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April  2009, 3(2): 253-270. doi: 10.3934/jmd.2009.3.253

Schrödinger operators defined by interval-exchange transformations

1. 

Department of Mathematics, Rice University, Houston, TX 77005, United States

Received  September 2008 Published  May 2009

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 nonconstant continuous sampling function.
Citation: Jon Chaika, David Damanik, Helge Krüger. Schrödinger operators defined by interval-exchange transformations. Journal of Modern Dynamics, 2009, 3 (2) : 253-270. doi: 10.3934/jmd.2009.3.253
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