Dynamics of the coquaternionic maps x^2 + bx - Falcão, M. I. (2023)
This paper deals with the dynamics of the one-parameter family of coquaternionic quadratic maps x2+ bx. By making use of recent results for the zeros of one-sided coquaternionic polynomials, the fixed points are analytically determined. The stability of these fixed points is also addressed, where, in some cases, due to the appearance of sets of non-isolated points, a suitably adapted notion of stability is used. The results obtained show clearly that this family is not dynamically equivalent to the simpler family x2+ c previously studied by the authors. Some numerical examples of other dynamics beyond fixed points are also presented.