Locally finite and locally nilpotent derivations with applications to polynomial flows, morphisms and 𝒢ₐ-actions. II

Abstract

This paper describes several applications of locally finite and locally nilpotent derivations; we recover the main results from the theory of polynomial flows, give a new inversion formula for polynomial automorphisms, reformulate the Eulerian conjecture for ordinary systems of differential equations in terms of locally nilpotent derivations, and give an algorithm to compute the invariant ring of a G a {\mathcal {G}_a} -action on affine n-space (if this ring is finitely generated).