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arXiv · 1302.5270

Spectrum of Lebesgue measure zero for Jacobi matrices of quasicrystals

Siegfried Beckus·Felix Pogorzelski
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Abstract

We study one-dimensional random Jacobi operators corresponding to strictly ergodic dynamical systems. In this context, we characterize the spectrum of these operators by non-uniformity of the transfer matrices and the set where the Lyapunov exponent vanishes. Adapting this result to subshifts satisfying the so-called Boshernitzan condition, it turns out that the spectrum is supported on a Cantor set with Lebesgue measure zero. This generalizes earlier results for Schrödinger operators.

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Siegfried Beckus, Felix Pogorzelski. 2013-02-21. Spectrum of Lebesgue measure zero for Jacobi matrices of quasicrystals. https://doi.org/10.1007/s11040-013-9131-4

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