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Papers by AJ Avila

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

Journal of Modern Dynamics, 2010

We show that given a fixed irrational rotation of the d-dimensional torus, any analytic SL(2, R) ... more We show that given a fixed irrational rotation of the d-dimensional torus, any analytic SL(2, R) cocycle can be perturbed so that the Lyapunov exponent becomes positive. This result strengthens and generalizes previous results of Krikorian [K] and Fayad-Krikorian [FK]. The key technique is the analiticity of m-functions (under the hypothesis of stability of zero Lyapunov exponents), first observed and used in the solution of the Ten Martini Problem [AJ]. In the appendix, we discuss the smoothness of m-functions for a larger class of systems including the skew-shift.

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

Journal of Modern Dynamics, 2010

We show that given a fixed irrational rotation of the d-dimensional torus, any analytic SL(2, R) ... more We show that given a fixed irrational rotation of the d-dimensional torus, any analytic SL(2, R) cocycle can be perturbed so that the Lyapunov exponent becomes positive. This result strengthens and generalizes previous results of Krikorian [K] and Fayad-Krikorian [FK]. The key technique is the analiticity of m-functions (under the hypothesis of stability of zero Lyapunov exponents), first observed and used in the solution of the Ten Martini Problem [AJ]. In the appendix, we discuss the smoothness of m-functions for a larger class of systems including the skew-shift.

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