For a prime p and a field $\mathbb{Z}_p$, is there support to find polynomials in $\mathbb{Z}_p[x]$ that can be iterated to generate all of $\mathbb{Z}_p$?
As an example that such exist, let p = 251 and consider $f(x) = 3x^3 + 3x^2+x+39 \in \mathbb{Z}_p[x]$. You can iterate this polynomial with any $x_0 \in \mathbb{Z}_p$, i.e., $x_{n+1} = f(x_n)$, and generate all of $\mathbb{Z}_p$.
I would appreciate any help identifying the theory about how such polynomials can be selected. Or even a topic / reference that gets me in the ballpark.