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arXiv · 1803.05157

No temporal distributional limit theorem for a.e. irrational translation

Dmitry Dolgopyat·Omri Sarig
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Abstract

Bromberg and Ulcigrai constructed piecewise smooth functions f on the torus such that the set of angles alpha for which the Birkhoff sums of f with respect to the irrational translation by alpha satisfies a temporal distributional limit theorem along the orbit of a.e. x has Hausdorff dimension one. We show that the Lebesgue measure of this set of angles is equal to zero.

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Dmitry Dolgopyat, Omri Sarig. 2018-03-14. No temporal distributional limit theorem for a.e. irrational translation. https://arxiv.org/abs/1803.05157

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