Abstract
LetV(θ) be a smooth, non-constant function on the torus and letT be a hyperbolic toral automorphism. Consider a discrete one dimensional Schrödinger operatorH, whose potential at sitej is given bygV j =gV(T j θ). We prove that wheng≧0 is small andg 1/2 ≦|E|≦2−g 1/2 , the Lyapunov exponent for the cocycle generated byH-E is proportional tog 2. The proof relies on a formula of Pastur and Figotin and on symbolic dynamics.
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