Fixed Points for Cubic Coquaternionic Maps

Abstract

This paper deals with the dynamics of a special twoparameter family of coquaternionic cubic maps. By making use of recent results for the zeros of one-sided coquaternionic polynomials, we analytically determine the fixed points of these maps. Some numerical examples illustrating the theory are also presented. The results obtained show an unexpected richness for the dynamics of cubic coquaternionic maps when compared to the already studied dynamics of quadratic maps.