Dolgopyat, Dmitry; Sarig, Omri
No temporal distributional limit theorem for a.e. irrational translation
Annales Henri Lebesgue, Volume 1  (2018), p. 127-148



Bromberg and Ulcigrai constructed piecewise smooth functions on the circle such that the set of α for which the sum k=0 n-1 f(x+kαmod1) 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 is equal to zero.


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