Spectral behavior of quasi periodic potentials

Spectral properties of Schrödinger operators of the type H _∊=-∆+∊ V, where ∆ is the Laplacian, V a quasiperiodic potential and ∊ a coupling constant, are developed. V is taken to be finite sum of exponentials with generic frequencies. For small ∊ a strong stability is shown. On the other hand, examples (in the finite diffeence case) are given, for which a transition in the type of spectrum occurs, as ∊ is increased.