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Normal Families of Bicomplex Holomorphic Functions

2008/06/26 by Kuldeep Singh Charak, Charak, K. S., Dominic Rochon +3
Mathematics · #Meromorphic and Entire Functions #Mathematics and Applications #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.0806.4403

Abstract

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 \boldj=0.

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