NORMAL FAMILIES OF BICOMPLEX HOLOMORPHIC FUNCTIONS-Reference-Cited by-同舟云学术

NORMAL FAMILIES OF BICOMPLEX HOLOMORPHIC FUNCTIONS

Published:2009-09 Issue:03 Volume:17 Page:257-268
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

CHARAK K. S.¹,ROCHON D.²,SHARMA N.¹

Affiliation:

1. Department of Mathematics, University of Jammu, Jammu-180 006, India

2. Département de mathématiques et d'informatique, Université du Québec, Trois-Rivières, C.P. 500 Trois-Rivières, Québec, Canada, G9A 5H7, Canada

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 j = 0.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X09004314

Reference19 articles.

1. Sur les suites infinies de fonctions

2. Normal Families

3. Normal Families of Meromorphic Functions

4. Normal families: New perspectives

5. Complexified clifford analysis

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