Towards a bifurcation theory for perturbed monomial dynamical systems modulo a prime

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We investigate perturbed monomial dynamical system over Fₚ given by iterations of x xⁿ+cp, where c∈ Fₚ. 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.