A Simple Proof of Jung's Theorem on Polynomial Automorphisms of $\C^2$

Nguyen Van Chau

paper

A Simple Proof of Jung's Theorem on Polynomial Automorphisms of $\C^2$

arXiv:math/0408077

Abstract

The Automorphism Theorem, discovered first by Jung in 1942, asserts that if $k$ is a field, then every polynomial automorphism of $k^{2}$ is a finite product of linear automorphisms and automorphisms of the form $(x, y) \mapsto (x + p (y), y)$ for $p \in k [y]$ . We present here a simple proof for the case $k=\C$ by using Newton-Puiseux expansions.