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- Title
Analytic Quasi-Perodic Cocycles with Singularities and the Lyapunov Exponent of Extended Harper's Model.
- Authors
Jitomirskaya, S.; Marx, C.
- Abstract
We show how to extend (and with what limitations) Avila's global theory of analytic SL(2,C) cocycles to families of cocycles with singularities. This allows us to develop a strategy to determine the Lyapunov exponent for the extended Harper's model, for all values of parameters and all irrational frequencies. In particular, this includes the self-dual regime for which even heuristic results did not previously exist in physics literature. The extension of Avila's global theory is also shown to imply continuous behavior of the LE on the space of analytic $${M_2(\mathbb{C})}$$-cocycles. This includes rational approximation of the frequency, which so far has not been available.
- Subjects
ANALYTIC functions; PERIODIC functions; MATHEMATICAL singularities; LYAPUNOV exponents; HEURISTIC algorithms; PHYSICS literature; APPROXIMATION theory
- Publication
Communications in Mathematical Physics, 2012, Vol 316, Issue 1, p237
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-012-1465-4