Dynamics of complex harmonic mappings
Complex Variables
2025-03-04 v3 Dynamical Systems
Abstract
This note initiates the study of the Fatou\,--\,Julia sets of a complex harmonic mapping. Along with some fundamental properties of the Fatou and the Julia sets, we observe some contrasting behaviour of these sets as those with in case of a holomorphic function. The existence of harmonic mapping with a wandering domain is also shown.
Keywords
Cite
@article{arxiv.2412.14924,
title = {Dynamics of complex harmonic mappings},
author = {Gopal Datt and Ramanpreet Kaur},
journal= {arXiv preprint arXiv:2412.14924},
year = {2025}
}