Fast and slow points of Birkhoff sums
Résumé
We investigate the growth rate of the Birkhoff sums $S_{n,\alpha}f(x)=\sum_{k=0}^{n-1}f(x+k\alpha)$, where $f$ is a continuous function with zero mean defined on the unit circle $\mathbb T$ and $(\alpha,x)$ is a ``typical'' element of $\mathbb T^2$. The answer depends on the meaning given to the word ``typical''. Part of the work will be done in a more general context.
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