Simon B., Zhu Y.F.
The Lyapunov exponents for Schr\"odinger operators with 
slowly oscillating potentials
(38K, AMSTeX)

ABSTRACT.  By studying the integrated density of states, we prove the 
existence of Lyapunov exponents and the Thouless formula for 
the Schr\"odinger operator $-d^2/ dx^2 + \cos x^{\nu}$ with 
$0< \nu < 1$ on $L^2[0,\infty)$. This yields an explicit formula 
for these Lyapunov exponents. By applying rank one perturbation 
theory, we also obtain some spectral consequences.