Law of large numbers for certain cylinder flows

Details Law of large numbers for certain cylinder flows Law of large numbers for certain cylinder flows

2011-08-17

arxiv.org/abs/1108.3519v2

Mathematics

Dynamical Systems

28 pages, 3 figures. Conditions of Theorem 1.2 improved

Scientific paper

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.

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