Definitions and Notation From Discrete Dynamics
Let S be a set and let F : S → S be a map from S to itself. The iterate of F with itself n times is denoted
A point P ∈ S is periodic if F(n)(P) = P for some n > 1.
The point is preperiodic if F(k)(P) is periodic for some k ≥ 1.
The (forward) orbit of P is the set
Thus P is preperiodic if and only if its orbit OF(P) is finite.
Read more about this topic: Arithmetic Dynamics
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