Continuity of the Lyapunov Exponent for analytic quasi-perodic cocycles with singularities

Abstract

We prove that the Lyapunov exponent of quasi-periodic cocyles with singularities behaves continuously over the analytic category. We thereby generalize earlier results, where singularities were either excluded completely or constrained by additional hypotheses. Applications are one-parameter families of analytic Jacobi operators, such as extended Harper's model describing crystals subject to external magnetic fields.

to appear in the Journal of Fixed Point Theory and Applications (JFPTA), 2011

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