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Zero measure Cantor spectra for continuum one-dimensional quasicrystals
Publikationstyp
Journal Article
Date Issued
2013-12-31
Sprache
English
Author(s)
Institut
TORE-URI
Volume
256
Issue
6
Start Page
1905
End Page
1926
Citation
Journal of Differential Equations 256 (6): 1905-1926 (2014)
Publisher DOI
Scopus ID
Publisher
Elsevier
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.
Subjects
Cantor spectrum of measure zero
Quasicrystals
Schrödinger operators
DDC Class
510: Mathematik