Abstract:Let ϕ : Fq → Fq be a rational map on a fixed finite field. We give explicit asymptotic formulas for the size of image sets ϕ n (Fq) as a function of n. This is done by using properties of the Galois groups of iterated maps, whose connection to the question of the size of image sets is established via Chebotarev's Density Theorem. We then apply these results to provide explicit bounds on the proportion of periodic points in Fq in terms of q for certain rational maps.
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.