English

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 j=0\bold{j}=0.

Keywords

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

R2 v1 2026-06-21T10:54:49.325Z