Let be a Rational Number in the Closed Interval , and generate a Sequence using the
Then the number of periodic Orbits of period (for Prime) is given by
(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
See also Tent Map
Ott, E. Chaos in Dynamical Systems. Cambridge: Cambridge University Press, pp. 26-31, 1993.
© 1996-9 Eric W. Weisstein