Work

Hénon maps with biholomorphic Kato surfaces

Year: 2025

Type: article

Abstract: 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\left (\mathbb {C}^2\right ) . 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.

Source: Communications of the American Mathematical Society

DOI: 10.1090/cams/53

Author: François Bacher

Institutions: Centre National de la Recherche Scientifique, Institut de Mathématiques de Bourgogne, Université Bourgogne Europe

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: Agence Nationale de la Recherche, Conseil régional de Bourgogne-Franche-Comté