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arXiv · 2604.27832

Two remarks on transcendental shift-like maps on $\mathbb{C}^N$

Ramanpreet Kaur
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Abstract

In \cite{Bedford}, the dynamics of a particular polynomial diffeomorphism of $\mathbb{C}^N$, called a polynomial shift-like map of type $\nu$, 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.

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Ramanpreet Kaur. 2026-04-30. Two remarks on transcendental shift-like maps on $\mathbb{C}^N$. https://arxiv.org/abs/2604.27832

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