The Repetition Property for Sequences on Tori Generated by Polynomials or Skew-Shifts

الأصل · EN

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 Schrödinger 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 Schrödinger operators with potentials generated by skew-shifts on tori that have, contrary to earlier belief, no eigenvalues.