Abstract
We introduce a renormalization procedure which allows us to study in a unified and concise way different properties of the irrational rotations on the unit circle \(\beta \mapsto \{\alpha + \beta\}\) , \(\alpha \in {\mathbb{R}}\!\setminus\! {\mathbb{Q}}\) . In particular, we obtain sharp results for the diffusion of the walk on \({\mathbb{Z}}\) generated by the location of points of the sequence {n α + β} on a binary partition of the unit interval. Finally, we give some applications of our method.
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Bonanno, C., Isola, S. A renormalization approach to irrational rotations. Annali di Matematica 188, 247–267 (2009). https://doi.org/10.1007/s10231-008-0074-5
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DOI: https://doi.org/10.1007/s10231-008-0074-5