A SIMPLE PROOF OF JUNG'S THEOREM ON POLYNOMIAL AUTOMORPHISMS OF  C²

Nguyen Van Chau

Abstract

           The Automorphism Theorem, discovered first by Jung in 1942, asserts that if  k  is a field, then every polynomial automorphism of k² is a finite product of linear automorphisms and automorphisms of the form (x, y) (x + p(y), y) for p ∈ k[y]. We present here a simple proof for the case k = C by using Newton-Puiseux expansions.