Copyright © 2010 Magali Marx and Hatem Najar. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study spectral properties of a family of quasiperiodic Schrödinger
operators on the real line in the adiabatic limit. We assume that the adiabatic iso-energetic
curve has a real branch that is extended along the momentum direction. In the energy intervals
where this happens, we obtain an asymptotic formula for the Lyapunov exponent and show
that the spectrum is purely singular. This result was conjectured and proved in a particular
case by Fedotov and Klopp (2005).