Hénon maps with biholomorphic Kato surfaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909777372643328 |
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| author | Bacher, François |
| author_facet | Bacher, François |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19547 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hénon maps with biholomorphic Kato surfaces Bacher, François Complex Variables Dynamical Systems 32A08, 32J15, 37F80 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. |
| title | Hénon maps with biholomorphic Kato surfaces |
| topic | Complex Variables Dynamical Systems 32A08, 32J15, 37F80 |
| url | https://arxiv.org/abs/2410.19547 |