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arXiv · 1410.0101

Cantor spectrum for a class of $C^2$ quasiperiodic Schrödinger operators

Yiqian Wang·Zhenghe Zhang
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Abstract

We show that for a class of $C^2$ quasiperiodic potentials and for any Diophantine frequency, the spectrum of the corresponding Schrödinger operators is Cantor. Our approach is of purely dynamical systems, which depends on a detailed analysis of asymptotic stable and unstable directions. We also apply it to general $\mathrm{SL}(2,\mathbb R)$ cocycles, and obtain that uniform hyperbolic systems form a open and dense set in some one-parameter family.

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Yiqian Wang, Zhenghe Zhang. 2014-10-01. Cantor spectrum for a class of $C^2$ quasiperiodic Schrödinger operators. https://arxiv.org/abs/1410.0101

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