Continuity of the Lyapunov exponent for analytic quasi-periodic cocycles with singularities

We prove that the Lyapunov exponent of quasi-periodic cocycles 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 include parameter dependent families of analytic Jacobi operators, such as extended Harper’s model describing crystals in varying lattice geometries subject to external magnetic fields.