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• W2776245874 abstract "In this paper, we prove the generic version of Cantor spectrum for quasi-periodic Schr{o}dinger operators with finitely smooth and small potentials, and we also show pure point spectrum for a class of multi-frequency $C^k$ long-range operators on $ell^2(Z^d)$. These results are based on reducibility properties of finitely differentiable quasi-periodic $SL(2,R)$ cocycles. More precisely, we prove that if the base frequency is Diophantine, then a $C^k$ $SL(2,R)$-valued cocycle is reducible if it is close to a constant cocycle, sufficiently smooth and the rotation number of it is Diophantine or rational with respect to the frequency." @default.
• W2776245874 created "2018-01-05" @default.
• W2776245874 creator A5004798549 @default.
• W2776245874 creator A5035894210 @default.
• W2776245874 date "2017-12-25" @default.
• W2776245874 modified "2023-09-24" @default.
• W2776245874 title "Reducibility of finitely differentiable quasi-periodic cocycles and its spectral applications" @default.
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• W2776245874 doi "https://doi.org/10.48550/arxiv.1712.09041" @default.
• W2776245874 hasPublicationYear "2017" @default.
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