Avila, Artur and Damanik, David (2005) Generic singular spectrum for ergodic Schrödinger operators. Duke Mathematical Journal, 130 (2). pp. 393-400. ISSN 0012-7094. doi:10.1215/S0012-7094-05-13035-6. https://resolver.caltech.edu/CaltechAUTHORS:20110513-104707967
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Abstract
We consider Schrödinger operators with ergodic potential V_ω(n) = f(T^n(ω)), n Є Z, ω Є Ω, where T : Ω → Ω is a nonperiodic homeomorphism. We show that for generic f Є 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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| Additional Information: | © 2005 Duke University Press. Received 3 September 2004. Revision received 24 February 2005. This work was done while Avila was visiting the California Institute of Technology. We thank Svetlana Jitomirskaya and Barry Simon for stimulating discussions. | |||||||||
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| Issue or Number: | 2 | |||||||||
| Classification Code: | 2000 Mathematics Subject Classification: Primary 82B44; Secondary 47B36 | |||||||||
| DOI: | 10.1215/S0012-7094-05-13035-6 | |||||||||
| Record Number: | CaltechAUTHORS:20110513-104707967 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20110513-104707967 | |||||||||
| Official Citation: | Generic Singular Spectrum For Ergodic Schrödinger Operators Artur Avila and David Damanik; 393-400 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 23659 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 13 May 2011 21:45 | |||||||||
| Last Modified: | 09 Nov 2021 16:16 |
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