Publisher DOI: 10.1016/j.jde.2013.12.003
Title: Zero measure Cantor spectra for continuum one-dimensional quasicrystals
Language: English
Authors: Lenz, Daniel 
Seifert, Christian  
Stollmann, Peter 
Keywords: Cantor spectrum of measure zero;Quasicrystals;Schrödinger operators
Issue Date: 31-Dec-2013
Publisher: Elsevier
Source: Journal of Differential Equations 256 (6): 1905-1926 (2014)
Abstract (english): 
We study Schrödinger operators on R with measures as potentials. Choosing a suitable subset of measures we can work with a dynamical system consisting of measures. We then relate properties of this dynamical system with spectral properties of the associated operators. The constant spectrum in the strictly ergodic case coincides with the union of the zeros of the Lyapunov exponent and the set of non-uniformities of the transfer matrices. This result enables us to prove Cantor spectra of zero Lebesgue measure for a large class of operator families, including many operator families generated by aperiodic subshifts. © 2013 Elsevier Inc.
URI: http://hdl.handle.net/11420/9575
ISSN: 1090-2732
Institute: Mathematik E-10 
Document Type: Article
Journal: Journal of differential equations 
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