We studyH=-d 2/dx 2+ V (x) withV (x) limit periodic, eg V (x)= Sa n cos (x/2 n) with S| an|< 8. We prove that for a genericV (and for generica n in the explicit example), s (H) is a Cantor (= nowhere dense, perfect) set. For a dense set, the spectrum is both Cantor and purely ...
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