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Creators/Authors contains: "Kanigowski, Adam"

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  1. ; ; ; (, International mathematics research notices)
    Accepted Manuscript Full Text Available
  2. ; ; (, Annals of Mathematics)
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  3. ; ; ; (, Inventiones mathematicae)
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  4. ; ; ; (, Israel Journal of Mathematics)
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  5. ; ; (, Journal of the American Mathematical Society)
    We study the spectral measures of conservative mixing flows on the 2 2 -torus having one degenerate singularity. We show that, for a sufficiently strong singularity, the spectrum of these flows is typically Lebesgue with infinite multiplicity. For this, we use two main ingredients: (1) a proof of absolute continuity of the maximal spectral type for this class of non-uniformly stretching flows that have an irregular decay of correlations, (2) a geometric criterion that yields infinite Lebesgue multiplicity of the spectrum and that is well adapted to rapidly mixing flows. 
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