Law of large numbers for certain cylinder flows
Dynamical Systems
2020-04-21 v3 Probability
Abstract
We construct new examples of cylinder flows, given by skew product extensions of irrational rotations on the circle, that are ergodic and rationally ergodic along a subsequence of iterates. In particular, they exhibit law of large numbers. This is accomplished by explicitly calculating, for a subsequence of iterates, the number of visits to zero, and it is shown that such number has a gaussian distribution.
Keywords
Cite
@article{arxiv.1108.3519,
title = {Law of large numbers for certain cylinder flows},
author = {Patricia Cirilo and Yuri Lima and Enrique Pujals},
journal= {arXiv preprint arXiv:1108.3519},
year = {2020}
}
Comments
25 pages, referee suggestions incorporated, to appear in Ergodic Theory and Dynamical Systems