Generic Singular Spectrum For Ergodic Schrödinger Operators
Avila, Artur ; Damanik, David
Duke Math. J., Tome 126 (2005) no. 1, p. 393-400 / Harvested from Project Euclid
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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
Publié le : 2005-11-01
Classification:  82B44,  47B36 
@article{1132064631,
     author = {Avila, Artur and Damanik, David},
     title = {Generic Singular Spectrum For Ergodic Schr\"odinger Operators},
     journal = {Duke Math. J.},
     volume = {126},
     number = {1},
     year = {2005},
     pages = { 393-400},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1132064631}
}

Avila, Artur; Damanik, David. Generic Singular Spectrum For Ergodic Schrödinger Operators. Duke Math. J., Tome 126 (2005) no. 1, pp.  393-400. http://gdmltest.u-ga.fr/item/1132064631/