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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2011
- DOI:
- 10.48550/arXiv.1106.6097
- arXiv:
- arXiv:1106.6097
- Bibcode:
- 2011arXiv1106.6097J
- Keywords:
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- Mathematics - Dynamical Systems;
- Mathematical Physics
- E-Print:
- to appear in the Journal of Fixed Point Theory and Applications (JFPTA), 2011