Strictly Ergodic Subshifts and Associated Operators
Dynamical Systems
2014-12-31 v1 Spectral Theory
Abstract
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.
Cite
@article{arxiv.math/0509197,
title = {Strictly Ergodic Subshifts and Associated Operators},
author = {David Damanik},
journal= {arXiv preprint arXiv:math/0509197},
year = {2014}
}
Comments
34 pages