Generic Singular Spectrum For Ergodic Schrödinger Operators

We consider Schrödinger operators with ergodic potential V ω ( n ) = f ( T n ( ω ) ) , n ∈ ℤ , ω ∈ Ω , where T : Ω → Ω is a nonperiodic 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