Unlikely intersections over finite fields: Polynomial orbits in small subgroups
László Mérai, Igor E. Shparlinski · Discrete and Continuous Dynamical Systems · 2019
We estimate the frequency of polynomial iterations which fall in a given multiplicative subgroup of a finite field of $ p $ elements. We also give a lower bound on the size of the subgroup which is multiplicatively generated by the first $ N $ elements in an orbit. We derive these from more general results about sequences of compositions on a fixed set of polynomials.