On a ''structure intermediate between quasiperiodic and random''

This paper proves rigorously that the structure factor of the ''structure intermediate between quasiperiodic and random'' introduced by Aubry, Godreche, and Luck is purely singular continuous apart from a delta function at zero for ''most'' choices of the parameters. The result is based on a proof that a flow under a step function over an irrational circle rotation is weakly mixing for ''most'' parameters, and on the Wonderland Theorem.