 2284 Sasa Kocic
 Singular continuous phase for Schroedinger operators over circle maps with breaks
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Dec 29, 22

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Abstract. We consider Schroedinger operators over a class of circle maps including C^{2+epsilon}smooth circle maps with finitely many break points. We show that in a region of the Lyapunov exponent  determined by the geometry of the dynamical partitions and alpha  the spectrum of Schroedinger operators over every such map, is purely singular continuous, for every alphaHoldercontinuous potential V. As a corollary, we obtain that for every sufficiently smooth such map, with an invariant measure mu and with rotation number in a set S, and mualmost all x in T^1, the corresponding Schroedinger operator has a purely continuous spectrum, for every Holdercontinuous potential V. Set S includes some Diophantine numbers of class D(delta), for any delta>1.
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