Mathematics – Dynamical Systems
Scientific paper
2007-08-23
Mathematics
Dynamical Systems
10 pages
Scientific paper
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.
Boshernitzan Michael
Damanik David
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