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

Abstract

We investigate perturbed monomial dynamical system over ${\mathbb{F}}_p$ given by iterations of $x\mapsto x^n+c\mathrm{mod}p$, 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.

Cited by in corpus (1)

• On the Number of Periodic Points of Quadratic Dynamical Systems Modulo a Prime