Normal Families of Bicomplex Holomorphic Functions
نویسندگان
چکیده
In this article, we introduce the concept of normal families of bicomplex holomorphic functions to obtain a bicomplex Montel theorem. Moreover, we give a general definition of Fatou and Julia sets for bicomplex polynomials and we obtain a characterization of bicomplex Fatou and Julia sets in terms of Fatou set, Julia set and filled-in Julia set of one complex variable. Some 3D visual examples of bicomplex Julia sets are also given for the specific slice j = 0.
منابع مشابه
Bicomplex algebra and function theory
This treatise investigates holomorphic functions defined on the space of bicomplex numbers introduced by Segre. The theory of these functions is associated with Fueter’s theory of regular, quaternionic functions. The algebras of quaternions and bicomplex numbers are developed by making use of so-called complex pairs. Special attention is paid to singular bicomplex numbers that lack an inverse. ...
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