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Zero-measure Cantor spectrum for Schrödinger operators with low-complexity potentials

Damanik, David and Lenz, Daniel (2006) Zero-measure Cantor spectrum for Schrödinger operators with low-complexity potentials. Journal de Mathématiques Pures et Appliquées, 85 (5). pp. 671-686. ISSN 0021-7824. doi:10.1016/j.matpur.2005.11.002. https://resolver.caltech.edu/CaltechAUTHORS:20170409-071347082

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Abstract

We consider discrete one-dimensional Schrödinger operators whose potentials belong to minimal subshifts of low combinatorial complexity and prove for a large class of such operators that the spectrum is a Cantor set of zero Lebesgue measure. This is obtained through an analysis of the frequencies of the subwords occurring in the potential. Our results cover most circle map and Arnoux–Rauzy potentials.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.matpur.2005.11.002DOIArticle
https://www.sciencedirect.com/science/article/pii/S0021782405001376PublisherArticle
ORCID:
AuthorORCID
Damanik, David0000-0001-5924-3849
Lenz, Daniel0000-0001-5820-475X
Additional Information:© 2005 Elsevier. Received 20 June 2005, Available online 13 December 2005. Supported in part by NSF grant DMS-0227289. We thank Artur Avila and Barry Simon for useful discussions. A substantial part of this work was done while one of the authors (D.L.) was visiting Caltech in September 2003. He would like to thank Barry Simon and the Department of Mathematics for the warm hospitality.
Funders:
Funding AgencyGrant Number
NSFDMS-0227289
Subject Keywords:Schrödinger operators; Cantor spectrum; Multiplicative ergodic theorem; Uniform cocycles
Issue or Number:5
Classification Code:MSC: 37A30; 47B39
DOI:10.1016/j.matpur.2005.11.002
Record Number:CaltechAUTHORS:20170409-071347082
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170409-071347082
Official Citation:David Damanik, Daniel Lenz, Zero-measure Cantor spectrum for Schrödinger operators with low-complexity potentials, Journal de Mathématiques Pures et Appliquées, Volume 85, Issue 5, 2006, Pages 671-686, ISSN 0021-7824, https://doi.org/10.1016/j.matpur.2005.11.002. (http://www.sciencedirect.com/science/article/pii/S0021782405001376)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76430
Collection:CaltechAUTHORS
Deposited By: 1Science Import
Deposited On:03 Apr 2018 20:38
Last Modified:15 Nov 2021 16:59

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