Singular perturbations with multiple poles of the simple polynomials

2016/06/18 by Xiao, Yingqing, Yang, Fei
#37F30 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary: 37F45 #Secondary: 37F10

paper · doi:10.48550/arxiv.1606.05757

Abstract

In this article, we study the dynamics of the following family of rational maps with one parameter: f_λ(z)= zⁿ+(λ²)/(zⁿ-λ), where n≥ 3 and λ∈ℂ^*. This family of rational maps can be viewed as a singular perturbations of the simple polynomial P_n(z)=zⁿ. We give a characterization of the topological properties of the Julia sets of the family f_λ according to the dynamical behaviors of the orbits of the free critical points.

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