Two remarks on transcendental shift-like maps on $\mathbb{C}^N$
Dynamical Systems
2026-05-01 v1 Complex Variables
Abstract
In \cite{Bedford}, the dynamics of a particular polynomial diffeomorphism of , called a polynomial shift-like map of type , has been studied as a higher dimensional analog of H\'enon maps. In this note, we prove that the Julia set of their transcendental counterpart is non-empty. In addition, an example of a transcendental shift-like map with an escaping wandering domain has been provided which, in fact, showcases a contrast with the dynamics of a polynomial shift map.
Keywords
Cite
@article{arxiv.2604.27832,
title = {Two remarks on transcendental shift-like maps on $\mathbb{C}^N$},
author = {Ramanpreet Kaur},
journal= {arXiv preprint arXiv:2604.27832},
year = {2026}
}