Polynomial maps that are roots of power series

TL;DR

This paper introduces polynomial maps called polynomial roots of power series, demonstrating their role in generating automorphism groups and characterizing such maps, especially in one dimension.

Contribution

It defines polynomial roots of power series and proves they generate automorphism groups, providing a detailed analysis in one dimension.

Findings

Polynomial roots of power series generate automorphism groups.

Characterization of origin-preserving polynomial maps as roots of power series.

Deeper analysis of the one-dimensional case.

Abstract

We introduce a class of polynomial maps that we call polynomial roots of powerseries, and show that automorphisms with this property generate the automorphism group in any dimension. In particular we determine generically which polynomial maps that preserve the origin are roots of powerseries. We study the one-dimensional case in greater depth.