No temporal distributional limit theorem for a.e. irrational translation
Dynamical Systems
2018-03-15 v1
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.
Cite
@article{arxiv.1803.05157,
title = {No temporal distributional limit theorem for a.e. irrational translation},
author = {Dmitry Dolgopyat and Omri Sarig},
journal= {arXiv preprint arXiv:1803.05157},
year = {2018}
}