Cubic Rational Maps with Escaping Critical Points, Part I: Julia Set Dichotomy in the Case of an Attracting Fixed Point

• Jun Hu ^[1] ; Arkady Etkin ^[2]
  1. [1] Brooklyn College of CUNY & Graduate Center of CUNY
  2. [2] Graduate Center of CUNY
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 3, 2022
• Idioma: inglés
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• Resumen

  • The Julia set of any quadratic rational map is either connected or a Cantor set. In this paper, we extend this dichotomy to any cubic rational map with all critical points escaping to an attracting fixed point.