## 2x mod 1 Map

Let be a Rational Number in the Closed Interval , and generate a Sequence using the Map

 (1)

Then the number of periodic Orbits of period (for Prime) is given by
 (2)

(i.e, the number of period- repeating bit strings, modulo shifts). Since a typical Orbit visits each point with equal probability, the Natural Invariant is given by
 (3)