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Density of positive Lyapunov exponents for quasiperiodic SL(2, R)-cocycles in arbitrary dimension

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  • We show that given a fixed irrational rotation of the $d$-dimensional torus, any analytic SL(2, R)-cocycle can be perturbed in such a way that the Lyapunov exponent becomes positive. This result strengthens and generalizes previous results of Krikorian [6] and Fayad-Krikorian [5]. The key technique is the analyticity of $m$-functions (under the hypothesis of stability of zero Lyapunov exponents), first observed and used in the solution of the Ten-Martini Problem [2].
    Mathematics Subject Classification: Primary: 34C20; Secondary: 37Cxx.

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