Density of positive Lyapunov exponents for quasiperiodic SL(2, R)-cocycles in arbitrary dimension
CNRS UMR 7586, Institut de Mathématiques de Jussieu, 175, Rue du Chevaleret, , 75013–Paris, France
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  and Fayad-Krikorian . 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 .
Mathematics Subject Classification: Primary: 34C20; Secondary: 37Cx.
Citation: Artur Avila. Density of positive Lyapunov exponents for quasiperiodic SL(2, R)-cocycles in arbitrary dimension. Journal of Modern Dynamics, 2009, 3 (4) : 631-636. doi: 10.3934/jmd.2009.3.631
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