8. A survey on iterations of mappings over finite fields
Rodrigo Martins, Daniel Panario, Claudio Qureshi · 2019
We survey iterations of polynomials and rational functions over finite fields. We show precise information on periodicity and permutational properties for some classical functions over finite fields including some quadratic polynomials, Chebyshev, Rédei, linearized and power maps. It seems hard to predict the periodicity behavior of functions over a finite field, so we provide heuristic arguments aiming at understanding their behavior in comparison to random uniform mappings over a finite field. We conclude showing a well-known methodology that provides many results about uniform random mappings.