Law of large numbers for certain cylinder flows - Cirilo, Patricia [UNESP]; Lima, Yuri; Pujals, Enrique (Cambridge University Press, 2014)
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 a 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.