Rotation Number Associated with Difference Equations Satisfied by Polynomials Orthogonal on the Unit Circle

The techniques of topological dynamics and differential-dynamical systems are used to study polynomials orthogonal with respect to a measure supported on the unit circle. It is assumed that the reflection coefficients associated with these polynomials form a stationary stochastic ergodic process. In particular, the techniques mentioned above are used to prove a gap labelling result.