Holomorphically conjugate polynomial automorphisms of C² are polynomially conjugate

2024/03/28 by Serge Cantat, Romain Dujardin, Cantat, Serge +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2403.19621

openalex publication_date 2024/03/28 · openalex created_date 2024/03/29 · openalex updated_date 2026/07/28

Abstract

We confirm a conjecture of Friedland and Milnor: if two polynomial automorphisms f and g in Aut(C²) with dynamical degree >1 are conjugate by some holomorphic diffeomorphism ϕof C², then ϕis a polynomial automorphism; thus, f and g are conjugate inside Aut(C²). We also discuss a number of variations on this result.

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