NORMAL FAMILIES OF BICOMPLEX HOLOMORPHIC FUNCTIONS

被引：25

作者：

Charak, K. S. ^{[2
]}

Rochon, D. ^{[1
]}

Sharma, N. ^{[2
]}

机构：

[1] Univ Quebec Trois Rivieres, Dept Math & Informat, Trois Rivieres, PQ G9A 5H7, Canada

[2] Univ Jammu, Dept Math, Jammu 180006, India

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2009年 / 17卷 / 03期

关键词：

Bicomplex Numbers; Complex Clifford Algebras; Normal Families; Montel Theorem; Bicomplex Dynamics; Julia Set; Fatou Set;

D O I：

10.1142/S0218348X09004314

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：257 / 268

页数：12

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