Orthogonal polynomials on the unit circle with Verblunsky coefficients   defined by the skew-shift
  I give an example of a family of orthogonal polynomials on the unit circle with Verblunsky coefficients given by the skew-shift for which the associated measures are supported on the entire unit circle and almost-every Aleksandrov measure is pure point.   Furthermore, I show in the case of the two dimensional skew-shift the zeros of para-orthogonal polynomials obey the same statistics as an appropriate irrational rotation.   The proof is based on an analysis of the associated CMV matrices. 
Helge Krueger
math.SP