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arXiv · 2410.19547

H\'enon maps with biholomorphic Kato surfaces

François Bacher
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Abstract

Let $F$ and $G$ be generalized H\'enon 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 X\'enelkis de H\'enon's survey. Moreover, we describe all the Kato surfaces associated to the germ of a generalized H\'enon map near infinity. We also show that two generalized H\'enon maps are conjugate near infinity, if and only if they are affinely conjugate.

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François Bacher. 2024-10-25. H\'enon maps with biholomorphic Kato surfaces. https://doi.org/10.1090/cams%2F53

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