Hénon maps with biholomorphic Kato surfaces

Let F F and G G be generalized Hénon maps. We show that the Kato surfaces associated to the germs of F F and G G near infinity are biholomorphic if and only if F F and G G are conjugate in A u t ( C 2 ) Aut (C^2 ) . This answers a question raised by Favre in the survey of Julia Xénelkis de Hénon [Arnold Math. J. 10 (2024), pp. 585–620]. 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.