On SL(2, R) valued smooth proximal cocycles and cocycles with positive Lyapunov exponents over irrational rotation flows
نویسنده
چکیده
Consider the class of C-smooth SL(2,R) valued cocycles, based on the rotation flow on the two torus with irrational rotation number α. We show that in this class, (i) cocycles with positive Lyapunov exponents are dense and (ii) cocycles that are either uniformly hyperbolic or proximal are generic, if α satisfies the following Liouville type condition: ∣ α− pn qn ∣ ∣ ≤ Cexp(−q n ), where C > 0 and 0 < κ < 1 are some constants and Pn qn is some sequence of irreducible fractions.
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