Almost reducibility and absolute continuity I

Abstract

We consider one-frequency analytic SL(2,R) cocycles. Our main result establishes the Almost Reducibility Conjecture in the case of exponentially Liouville frequencies. Together with our earlier work, this implies that all cocycles close to constant are almost reducible, independent of the frequency. In our forthcoming work, we discuss applications to the analysis of the absolutely continuous spectrum of one-frequency Schrodinger operators.