Hénon maps with biholomorphic Kato surfaces

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.

One section and one result added, to adress surjection properties

References in corpus (2)

• Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents
• Logarithmic Moduli Spaces for Surfaces of Class VII