## Duke Mathematical Journal

### Generic Singular Spectrum For Ergodic Schrödinger Operators

#### Abstract

We consider Schrödinger operators with ergodic potential $V_\omega(n)=f(T^{n}(\omega))$, $n \in \bb{Z}$, $\omega \in \Omega$, where $T:\Omega \to \Omega$ is a nonperiodic homeomorphism. We show that for generic $f \in C(\Omega)$, the spectrum has no absolutely continuous component. The proof is based on approximation by discontinuous potentials which can be treated via Kotani theory

#### Article information

Source
Duke Math. J. Volume 130, Number 2 (2005), 393-400.

Dates
First available: 15 November 2005

http://projecteuclid.org/euclid.dmj/1132064631

Digital Object Identifier
doi:10.1215/S0012-7094-05-13035-6

Mathematical Reviews number (MathSciNet)
MR2181094

#### Citation

Avila, Artur; Damanik, David. Generic Singular Spectrum For Ergodic Schrödinger Operators. Duke Mathematical Journal 130 (2005), no. 2, 393--400. doi:10.1215/S0012-7094-05-13035-6. http://projecteuclid.org/euclid.dmj/1132064631.

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