A preperiodic point of a map 
is an element 
whose map orbit contains
only a finite number of distinct points.
Equivalently,
 |
for some integers 
and 
, where 
denotes 
-fold function composition
and 
is the identity map (Silverman 2010, pp. 2-3).
After 
iterations, the map orbit
enters a periodic orbit.
Every periodic point is preperiodic, but the converse need not hold. For the map 
given by 
, the point 
is preperiodic because 
, but it is not a periodic
point.
