A renormalization approach to irrational rotations

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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.
27 pages

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Dynamical Systems, Number Theory, 37E05, 37A25, 37A45

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http://salesiana.dossiersoluciones.com/handle/123456789/135399

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0708.0048
 http://arxiv.org/abs/0708.0048

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arXiv