Holomorphically conjugate polynomial automorphisms of C 2 $\mathbb {C}^2$ are polynomially conjugate

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2024-09-26 DOI:10.1112/blms.13164

Serge Cantat, Romain Dujardin

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引用次数: 0

Abstract

We confirm a conjecture of Friedland and Milnor: if two polynomial automorphisms $f$ and $g \in Aut (A_{C}^{2})$ with dynamical degree greater than 1 are conjugate by some holomorphic diffeomorphism $φ : C^{2} \to C^{2}$ , then $φ$ is a polynomial automorphism; thus, $f$ and $g$ are conjugate inside $Aut (A_{C}^{2})$ . We also discuss a number of variations on this result.

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c2 $\mathbb {C}^2$的全纯共轭多项式自同构是多项式共轭的

我们证实弗里德兰和米尔诺的一个猜想：如果两个多项式自同构f $f$和g∈Aut (a2) $g\in \mathsf {Aut}(\mathbb {A}^2_\mathbf {C})$的动态度大于1是共轭的由某全纯微分同构φ：c2→c2 $\varphi \colon \mathbf {C}^2\rightarrow \mathbf {C}^2$，则φ $\varphi$是多项式自同构；因此，f $f$和g $g$在Aut (ac2) $\mathsf {Aut}(\mathbb {A}^2_\mathbf {C})$内共轭。我们还讨论了这个结果的一些变化。

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