06-120 Bassam R. Fayad, Alistair J. Windsor

A Dichotomy between Discrete and Continuous Spectrum for a Class of Special Flows over Rotations. (296K, PDF) Apr 18, 06

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Abstract. We provide sufficient conditions on a positive function so that the associated special flow over any irrational rotation is either weak mixing or $L^2$-conjugate to a suspension flow. This gives the first such complete classification within the class of Liouville dynamics. This rigidity coexists with a plethora of pathological behaviors.

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