Last Y., Simon B.
Modified Pr\"ufer and EFGP Transforms and deterministic models 
with dense point spectrum
(38K, AMSTeX)

ABSTRACT.  We provide a new proof of the theorem of Simon and Zhu 
that in the region $|E| < \lambda$ for a.e.~energies, 
$-\frac{d^2}{dx^2}+\lambda \cos (x^\alpha)$, $0<\alpha <1$ has 
Lyapunov behavior with a quasi-classical formula for the 
Lyapunov exponent. We also prove Lyapunov behavior for a.e.~$E
\in [-2,2]$ for the discrete model with $V(j^2) = e^j$, $V(n)=0$ 
if $n\notin \{1,4,9,\dots \}$. The arguments depend on a direct 
analysis of the equations for the norm of a solution.