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 bar right arrow {alpha + beta}, alpha is an element of R\Q. In particular, we obtain sharp results for the diffusion of the walk on Z generated by the location of points of the sequence {n alpha + beta} on a binary partition of the unit interval. Finally, we give some applications of our method.
A renormalization approach to irrational rotations
BONANNO, CLAUDIO;
2009-01-01
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 bar right arrow {alpha + beta}, alpha is an element of R\Q. In particular, we obtain sharp results for the diffusion of the walk on Z generated by the location of points of the sequence {n alpha + beta} on a binary partition of the unit interval. Finally, we give some applications of our method.File in questo prodotto:
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