Fractals/Mathematics/rotating

Rotation map defines dynamical systems on the circle ( maps of the circle to itself = self-maps on the circle). The theory describing it is called Rotation Theory

"If a is rational, then every point is periodic. If a is irrational, then every point has a dense orbit." David Richeson

rational
Rotation map  $$R$$ describes counterclockwise rotation of point $$ \theta$$ thru   $$ \frac{p}{q}$$ turns on the unit circle:

$$ R_{\frac{p}{q}}(\theta) = \theta + \frac{p}{q} $$

It is used for computing:
 * itinerary

irrational

 * ROTATE IN A CIRCLE WITH A ROTATION by  Sylvie Ruette (in fr.)
 * Wikipedia: Irrational rotation

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