Normal Families of Bicomplex Holomorphic Functions
Complex Variables
2011-01-20 v5 Dynamical Systems
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 .
Cite
@article{arxiv.0806.4403,
title = {Normal Families of Bicomplex Holomorphic Functions},
author = {K. S. Charak and D. Rochon and N. Sharma},
journal= {arXiv preprint arXiv:0806.4403},
year = {2011}
}
Comments
20 pages, 9 figures