04-166 David Damanik and Rowan Killip

Almost Everywhere Positivity of the Lyapunov Exponent for the Doubling Map (13K, LaTeX) May 25, 04

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Abstract. We show that discrete one-dimensional Schr\"odinger operators on the half-line with ergodic potentials generated by the doubling map on the circle, $V_\theta(n) = f(2^n \theta)$, 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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