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

Nguyen Van Chau
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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.

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Nguyen Van Chau. 2004-08-05. A Simple Proof of Jung's Theorem on Polynomial Automorphisms of $\C^2$. https://arxiv.org/abs/math/0408077

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