Abstract
We show that discrete one-dimensional Schrödinger operators on the half-line with ergodic potentials generated by the doubling map on the circle, V θ (n)=f(2nθ), may be realized as the half-line restrictions of a non-deterministic family of whole-line operators. As a consequence, the Lyapunov exponent is almost everywhere positive and the absolutely continuous spectrum is almost surely empty.
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Communicated by B. Simon
D. D. was supported in part by NSF grant DMS–0227289.
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Damanik, D., Killip, R. Almost Everywhere Positivity of the Lyapunov Exponent for the Doubling Map. Commun. Math. Phys. 257, 287–290 (2005). https://doi.org/10.1007/s00220-004-1261-x
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DOI: https://doi.org/10.1007/s00220-004-1261-x