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

• rotation maps
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irrational

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

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