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arXiv · 0708.0048

A renormalization approach to irrational rotations

Claudio Bonanno·Stefano Isola
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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 $β\mapsto \set{α+β}$, $α\in \R\setminus \Q$. In particular we obtain sharp results for the diffusion of the walk on $\Z$ generated by the location of points of the sequence $\{nα+β\}$ on a binary partition of the unit interval. Finally we give some applications of our method.

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Claudio Bonanno, Stefano Isola. 2007-07-31. A renormalization approach to irrational rotations. https://arxiv.org/abs/0708.0048

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