  This paper deals with general structural properties of one-dimensional
Schr"odinger operators with some absolutely continuous spectrum. The basic
result says that the omega limit points of the potential under the shift map
are reflectionless on the support of the absolutely continuous part of the
spectral measure. This implies an Oracle Theorem for such potentials and
Denisov-Rakhmanov type theorems.
  In the discrete case, for Jacobi operators, these issues were discussed in my
recent paper [19]. The treatment of the continuous case in the present paper
depends on the same basic ideas.
