Singular Perturbations with Multiple Poles of the Simple Polynomials

• Yingqing Xiao ^[1] ; Fei Yang ^[2]
  1. [1] Hunan University

     Hunan University

     China

     
  2. [2] Nanjing University

     Nanjing University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 16, Nº 3, 2017, págs. 731-747
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.