, Volume 288, Issue 3, pp 907-918
Date: 27 Nov 2008

On the Spectrum and Lyapunov Exponent of Limit Periodic Schrödinger Operators

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.

Communicated by B. Simon