# Nonarchimedean dynamical systems and formal groups

## TL;DR

This paper proves theorems confirming that certain commuting $p$-adic power series are related to formal groups, either as endomorphisms or semi-conjugate, advancing understanding of nonarchimedean dynamical systems.

## Contribution

It establishes conditions under which commuting $p$-adic power series correspond to formal group endomorphisms or semi-conjugates, confirming Lubin's observation.

## Key findings

- Existence of a formal group associated with commuting power series
- Conditions under which power series are endomorphisms or semi-conjugate
- Advancement in understanding nonarchimedean dynamical systems

## Abstract

We prove two theorems that confirm an observation of Lubin concerning families of $p$-adic power series that commute under composition: under certain conditions, there is a formal group such that the power series in the family are either endomorphisms of this group, or semi-conjugate to endomorphisms of this group.