Preperiodic points of polynomial dynamical systems over finite fields

For a prime p, positive integers Formula: see text, and a polynomial f with coefficients in Formula: see text, let Formula: see text. As n varies, the Formula: see text partition the set of strictly preperiodic points of the dynamical system induced by the action of f on Formula: see text. In this paper, we compute statistics of strictly preperiodic points of dynamical systems induced by unicritical polynomials over finite fields by obtaining effective upper bounds for the proportion of Formula: see text lying in a given Formula: see text. Moreover, when we generalize our definition of Formula: see text, we obtain both upper and lower bounds for the resulting averages.