English

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 CN\mathbb{C}^N, called a polynomial shift-like map of type ν\nu, 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}
}
R2 v1 2026-07-01T12:43:33.467Z