Generic singular continuous spectrum for ergodic Schrödinger operators
Artur Avila, David Damanik
Abstract
We consider Schrödinger operators with ergodic potential Vω(n)=f(Tn(ω)), n ∈ , ω∈ Ω, where T:Ω Ω is a non-periodic homeomorphism. We show that for generic f ∈ C(Ω), the spectrum has no absolutely continuous component. The proof is based on approximation by discontinuous potentials which can be treated via Kotani Theory.
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