Spectral gaps of almost Mathieu operators in the exponential regime
Wencai Liu
Fudan University, Shanghai, ChinaXiaoping Yuan
Fudan University, Shanghai, China
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Abstract
For almost Mathieu operator
the dry version of the Ten Martini Problem predicts that the spectrum of has all gaps open for all and . Avila and Jitomirskaya prove that has all gaps open for Diophantine and . In the present paper, we show that has all gaps open for all with small .
Cite this article
Wencai Liu, Xiaoping Yuan, Spectral gaps of almost Mathieu operators in the exponential regime. J. Fractal Geom. 2 (2015), no. 1, pp. 1–51
DOI 10.4171/JFG/15