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.

11 pages

References in corpus (4)

• Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrodinger operators
• The absolutely continuous spectrum of the almost Mathieu operator
• Global theory of one-frequency Schrodinger operators I: stratified analyticity of the Lyapunov exponent and the boundary of nonuniform hyperbolicity
• Holder continuity of absolutely continuous spectral measures for one-frequency Schrodinger operators

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