Mathematical Physics, Analysis and Geometry

, Volume 16, Issue 3, pp 289–308 | Cite as

Spectrum of Lebesgue Measure Zero for Jacobi Matrices of Quasicrystals

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Abstract

We study one-dimensional random Jacobi operators corresponding to strictly ergodic dynamical systems. We characterize the spectrum of these operators via non-uniformity of the transfer matrices and vanishing of the Lyapunov exponent. For aperiodic, minimal subshifts satisfying the so-called Boshernitzan condition this gives that the spectrum is supported on a Cantor set with Lebesgue measure zero. This generalizes earlier results for Schrödinger operators.

Keywords

Jacobi operator Cantor spectrum Lyapunov exponent Dynamical system Aperiodic subshift 

Mathematics Subject Classification (2010)

81Q10 47B80 37A30 52C23 
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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Fakultät für Mathematik und Informatik, Mathematisches Institut, Lehrstuhl AnalysisFriedrich-Schiller-Universität JenaJenaGermany

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