Lenz, DanielDanielLenzSeifert, ChristianChristianSeifertStollmann, PeterPeterStollmann2021-05-202021-05-202013-12-31Journal of Differential Equations 256 (6): 1905-1926 (2014)http://hdl.handle.net/11420/9575We 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.en1090-27322013619051926ElsevierCantor spectrum of measure zeroQuasicrystalsSchrödinger operatorsMathematikJournal Article10.1016/j.jde.2013.12.003Journal Article