Resumen de Singular Perturbations with Multiple Poles of the Simple Polynomials

Yingqing Xiao, Fei Yang

• In this article, we study the dynamics of the following family of rational maps with one parameter:

  fλ(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 Pn(z) = zn. We give a characterization of the topological properties of the Julia sets of the family fλ according to the dynamical behaviors of the orbits of the free critical points.