Dynamics of a family of meromorphic functio

Alex Rodríguez Reverter ^[1]
1. [1] Universitat de Barcelona
  
  Universitat de Barcelona
  
  Barcelona, España
Localización: Reports@SCM: an electronic journal of the Societat Catalana de Matemàtiques, ISSN-e 2385-4227, Vol. 7, Nº. 1, 2022, págs. 41-49
Idioma: inglés
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Resumen
- català
  En aquest projecte estudiem el comportament dinamic de la famlia de funcions transcendents meromorfes f(z) = ez z+1 1, la qual es pot veure com l'analeg meromorf de la ben coneguda famlia de polinomis cubics de Milnor Pa(z) = z2(z a) [12] o la seva versio entera z2ez [7, 8]. Contrariament a aquests dos casos, les conques d'atraccio de f no son simplement connexes. De fet, en aquest document es demostra que sota certes condicions, la conca d'atraccio de z = 0 es in nitament connexa.
- català
  In this paper we analyze the dynamical behavior of the family of transcendental meromorphic maps f(z) = ez z+1 1 . This family is the meromorphic analogue of the well-known Milnor family of cubic polynomials Pa(z) = z2(z a) [12] or its entire version z2ez [7, 8]. Opposed to these two cases, the basins of attraction of f are not simply connected. In fact, we prove that under certain conditions, the basin of attraction of z = 0 is in nitely connected