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arXiv · 1609.03757

Lebesgue spectrum of countable multiplicity for conservative flows on the torus

Bassam Fayad·Giovanni Forni·Adam Kanigowski
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Abstract

We study the spectral measures of conservative mixing flows on the 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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Bassam Fayad, Giovanni Forni, Adam Kanigowski. 2016-09-13. Lebesgue spectrum of countable multiplicity for conservative flows on the torus. https://arxiv.org/abs/1609.03757

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