We investigate perturbed monomial dynamical system over $\mathbb{ F}_p$ given by iterations of $x\mapsto x^n+c\bmod{ p}$, where $c\in \mathbb{ F}_p$. Instead of study the systems one at a time we study all of them at the same time. The complex distibution of periodic points is visualized in the so called Periodic Point Diagram, which can be seen as a discrete version of the classical Bifurcation Diagram. We also prove some general results about the distribution of periodic points. We end the article with a conjecture about the total number of periodic points.
Categories: math.DS math.NT