ON A STRUCTURE INTERMEDIATE BETWEEN QUASI-PERIODIC AND RANDOM

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