Connectivity of Julia sets of Newton maps: a unified approach

• Krzysztof Barański ^[1] ; Núria Fagella ^[2] ; Xavier Jarque ^[2] ; Bogusława Karpińska ^[3]
  1. [1] University of Warsaw

     University of Warsaw

     Warszawa, Polonia

     
  2. [2] Universitat de Barcelona

     Universitat de Barcelona

     Barcelona, España

     
  3. [3] Warsaw University of Technology

     Warsaw University of Technology

     Warszawa, Polonia

     

  Mostrar afiliaciones +
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 3, 2018, págs. 1211-1228
• Idioma: inglés
• DOI: 10.4171/RMI/1022
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper we present a unified proof of the fact that the Julia set of Newton’s method applied to a holomorphic function on the complex plane (a polynomial of degree larger than 1 or a transcendental entire function) is connected. The result was recently completed by the authors’ previous work, as a consequence of a more general theorem whose proof spreads among many papers, which consider separately a number of particular cases for rational and transcendental maps, and use a variety of techniques. In this note we present a unified, direct and reasonably self-contained proof which works in all situations alike.