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arXiv · 0807.4339

On the spectrum and Lyapunov exponent of limit periodic Schrodinger operators

Artur Avila
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Abstract

We exhibit a dense set of limit periodic potentials for which the corresponding one-dimensional Schrödinger operator has a positive Lyapunov exponent for all energies and a spectrum of zero Lebesgue measure. No example with those properties was previously known, even in the larger class of ergodic potentials. We also conclude that the generic limit periodic potential has a spectrum of zero Lebesgue measure.

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Artur Avila. 2008-07-28. On the spectrum and Lyapunov exponent of limit periodic Schrodinger operators. https://doi.org/10.1007/s00220-008-0667-2

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