Preperiodic points of polynomial dynamical systems over finite fields.

For a prime p, positive integers r , n , and a polynomial f with coefficients in p r , let W p , r , n (f) = f n p r \ f n + 1 p r . As n varies, the W p , r , n (f) partition the set of strictly preperiodic points of the dynamical system induced by the action of f on p r . 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 p r lying in a given W p , r , n (f). Moreover, when we generalize our definition of W p , r , n (f) , we obtain both upper and lower bounds for the resulting averages. [ABSTRACT FROM AUTHOR]