Parámetros especiales y deformaciones lineales de la familia \( (\wp(z))^2 + c \): Special parameters and linear deformations of the family \( (\wp(z))^2 + c \)

Adrián Esparza-Amador

doi:10.56754/0719-0646.2702.307

DOI:

https://doi.org/10.56754/0719-0646.2702.307

Abstract

In this work, we examine the space of parameters of a family of elliptic functions of order four. For the case of square, rectangular, and triangular lattices, we determine parameters for which the Fatou set is empty, consists of an attractive component, or consists of a parabolic component.

Resumen

En este trabajo, examinamos el espacio de parámetros de una familia de funciones elípticas de orden cuatro. Para el caso de retículas cuadradas, rectangulares y triangulares, determinamos parámetros para los cuales el conjunto de Fatou es vacío, consta de una componente atractora, o bien consta de una componente parabólica.

Keywords

Dynamics of meromorphic functions , Fatou and Julia sets , quasiconformal mappings

Mathematics Subject Classification:

37F10 , 33E05 , 37F31

Adrián Esparza-Amador Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia, Chile. https://orcid.org/0000-0002-7544-9203

Pages: 307–327
Date Published: 2025-10-06
In Press

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