Uniform spectral properties of one-dimensional quasicrystals, iv. quasi-sturmian potentials

被引：0
作者：
David Damanik
Daniel Lenz
机构：
[1] University of California,Department of Mathematics
[2] The Hebrew University of Jerusalem,Institute of Mathematics
[3] Johann Wolfgang Goethe-UniversitÄt,Fachbereich Mathematik
来源：
Journal d’Analyse Mathématique | 2003年 / 90卷
关键词：
Lyapunov Exponent; Spectral Type; Rotation Number; Lebesgue Measure Zero; Pure Point Spectrum;
D O I：
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中图分类号：
学科分类号：
摘要：
We consider discrete one-dimensional Schrödinger operators with quasi-Sturmian potentials. We present a new approach to the trace map dynamical system which is independent of the initial conditions and establish a characterization of the spectrum in terms of bounded trace map orbits. Using this, it is shown that the operators have purely singular continuous spectrum and their spectrum is a Cantor set of Lebesgue measure zero. We also exhibit a subclass having purely α-continuous spectrum. All these results hold uniformly on the hull generated by a given potential.
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页码：115 / 139
页数：24
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