Holomorphically conjugate polynomial automorphisms of C^2 are polynomially conjugate
Dynamical Systems
2024-03-29 v1 Complex Variables
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.
Cite
@article{arxiv.2403.19621,
title = {Holomorphically conjugate polynomial automorphisms of C^2 are polynomially conjugate},
author = {Serge Cantat and Romain Dujardin},
journal= {arXiv preprint arXiv:2403.19621},
year = {2024}
}