Classification of one-dimensional superattracting germs in positive characteristic

TL;DR

This paper classifies one-dimensional superattracting germs over fields of positive characteristic, showing formal and analytic classifications align, and extends some results to higher dimensions.

Contribution

It provides a comprehensive classification of superattracting germs in positive characteristic, including a higher-dimensional extension.

Findings

Formal and analytic classifications coincide for these germs

Complete classification of superattracting germs in one dimension

Extension of results to higher dimensions

Abstract

We give a classification of superattracting germs in dimension one over a complete normed algebraically closed field of positive characteristic up to conjugacy. In particular we show that formal and analytic classifications coincide for these germs. We also give a higher dimensional version of some of these results.