Singular perturbations of zⁿ with a pole on the unit circle

Abstract

We consider the family of complex maps given by fλ,a (z) = z n + λ/(z - a)d where n, d ≥ 1 are integers, and a and λ are complex parameters such that a = 1 and is sufficiently small. We focus on the topological characteristics of the Julia and Fatou sets of fλ,a.