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arXiv · 2403.19621

Holomorphically conjugate polynomial automorphisms of C^2 are polynomially conjugate

Serge Cantat·Romain Dujardin
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Abstract

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

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Serge Cantat, Romain Dujardin. 2024-03-28. Holomorphically conjugate polynomial automorphisms of C^2 are polynomially conjugate. https://arxiv.org/abs/2403.19621

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