**
Below is the ascii version of the abstract for 97-368.
The html version should be ready soon.**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.