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

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

2011-06-30

arxiv.org/abs/1106.6097v1

J. Fixed Point Theory Appl. 10 (2011), 129-146

Mathematics

Dynamical Systems

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

Scientific paper

10.1007/s11784-011-0055-y

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.

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