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arXiv · 2608.14042

On automorphisms of super-level sets of Green's functions of H\'{e}non maps

Mahima·Ratna Pal
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Abstract

The aim of this article is two-fold. First, we obtain a normal form for automorphisms of the escaping sets of H\'{e}non maps in a neighborhood of the attracting fixed point at infinity. Building on this local description, we characterize the global automorphisms of $\mathbb{C}^2$ that preserve the escaping sets. The analytic structure of the escaping sets, as established by Hubbard--Oberste-Vorth (\cite{HOV}), plays a crucial role in the proof of these results. In a similar spirit, we investigate the analytic structure of the super-level sets of the Green's functions associated with H\'{e}non maps and give a description of the automorphisms of these domains.

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Mahima, Ratna Pal. 2026-08-14. On automorphisms of super-level sets of Green's functions of H\'{e}non maps. https://arxiv.org/abs/2608.14042

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