A renormalization approach to irrational rotations

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 , . In particular, we obtain sharp results for the diffusion of the walk on generated by the location of points of the sequence { n α + β...

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Bibliographic Details
Published in:Annali di matematica pura ed applicata 2009, Vol.188 (2), p.247-267
Main Authors: Bonanno, Claudio, Isola, Stefano
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary: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 , . In particular, we obtain sharp results for the diffusion of the walk on 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.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-008-0074-5