Abstract
We prove rotations-reducibility for close to constant quasi-periodic SL(2,R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$SL(2,\\mathbb {R})$$\\end{document} cocycles in one frequency in the finite regularity and smooth cases, and derive some applications to quasi-periodic Schrödinger operators.
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