Hénon maps with biholomorphic Kato surfaces

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.