Artur Avila, Konstantin Khanin, Martin Leguil
Published 2020-04-20Version 1
In this paper we study spectral properties of Schr\"odinger operators with quasi-periodic potentials related to quasi-periodic action minimizing trajectories for analytic twist maps. We prove that the spectrum contains a component of absolutely continuous spectrum provided that the corresponding trajectory of the twist map belongs to an analytic invariant curve.
Invariant graphs of rational maps
Cantor Spectrum for Schrödinger Operators with Potentials arising from Generalized Skew-shifts
Uniformity Aspects of $\mathrm{SL}(2,\mathbb{R})$ Cocycles and Applications to Schrödinger Operators Defined Over Boshernitzan Subshifts
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