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This Arbeitsgemeinschaft discussed the spectral properties of quasi-periodic Schrödinger operators in one space dimension. After presenting background material on Schrödinger operators with dynamically defined potentials and some results about certain classes of dynamical systems, the recently developed global theory of analytic one-frequency potentials was discussed in detail. This was supplemented by presentations on an important special case, the almost Mathieu operator, and results showing phenomena exhibited outside the analytic category.
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Artur Avila, David Damanik, Svetlana Jitomirskaya, Arbeitsgemeinschaft: Quasiperiodic Schrödinger Operators. Oberwolfach Rep. 9 (2012), no. 2, pp. 1035–1106DOI 10.4171/OWR/2012/17