  The repetition property of a sequence in a metric space, a notion introduced
by us in an earlier paper, is of importance in the spectral analysis of ergodic
Schr\"odinger operators. It may be used to exclude eigenvalues for such
operators. In this paper we study the question of when a sequence on a torus
that is generated by a polynomial or a skew-shift has the repetition property.
This provides classes of ergodic Schr\"odinger operators with potentials
generated by skew-shifts on tori that have, contrary to earlier belief, no
eigenvalues.
