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arXiv · 2410.19547

Hénon maps with biholomorphic Kato surfaces

François Bacher
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Abstract

Let $F$ and $G$ be generalized Hénon maps. We show that the Kato surfaces associated to the germs of $F$ and $G$ near infinity are biholomorphic if and only if $F$ and $G$ are conjugate in $\text{Aut}(\mathbb{C}^2)$. This answers a question raised by Favre in Xénelkis de Hénon's survey. Moreover, we describe all the Kato surfaces associated to the germ of a generalized Hénon map near infinity. We also show that two generalized Hénon maps are conjugate near infinity, if and only if they are affinely conjugate.

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François Bacher. 2025-09-09. Hénon maps with biholomorphic Kato surfaces. https://doi.org/10.1090/cams%2F53

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