A renormalization approach to irrational rotations
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 α+β, α ∈ . In particular we obtain sharp results for the diffusion of the walk on 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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