Almost reducibility of quasiperiodic sl(2, R)-cocycles in ultradifferentiable classes
Abstract
Given a quasiperiodic cocycle in sl(2, R) sufficiently close to a constant, we prove that it is almost-reducible in ultradifferentiable class under an adapted arithmetic condition on the frequency vector. We also give a corollary on the H\"older regularity of the Lyapunov exponent.
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