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Dyadic transformation

A dyadic transformation is a mapping $d: \R \to \R^\infty,$ produced by the rule $x_0 \in [0, 1]$ and $x_{i+1} = 2x_i \mod 2$ for all i.

If $x 0$ is rational, the image will be a finite subset of $[0,1]$ (for odd denominators a finite cyclic group), for irrational ones a ?dense subset?.

Categories: Dynamical systems

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07-14-2008 23:18:10
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