Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation

Abstract

We show that the 1-dimensional Schrodinger equation with a quasiperiodic potential which is analytic on its hull admits a Floquet representation for almost every energyE in the upper part of the spectrum. We prove that the upper part of the spectrum is purely absolutely continuous and that, for a generic potential, it is a Cantor set. We also show that for a small potential these results extend to the whole spectrum.