Strictly Ergodic Subshifts and Associated Operators

Details Strictly Ergodic Subshifts and Associated Operators Strictly Ergodic Subshifts and Associated Operators

2005-09-08

arxiv.org/abs/math/0509197v1

Mathematics

Dynamical Systems

34 pages

Scientific paper

We consider ergodic families of Schr\"odinger operators over base dynamics given by strictly ergodic subshifts on finite alphabets. It is expected that the majority of these operators have purely singular continuous spectrum supported on a Cantor set of zero Lebesgue measure. These properties have indeed been established for large classes of operators of this type over the course of the last twenty years. We review the mechanisms leading to these results and briefly discuss analogues for CMV matrices.

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