Substitution maps in the Robba ring

TL;DR

This paper investigates substitution maps within the Robba ring, addressing questions motivated by p-adic Hodge theory and dynamical systems, and extends existing results in special cases.

Contribution

It provides new insights and generalizations regarding substitution maps in the Robba ring, building on prior work by Kedlaya, Colmez, and others.

Findings

Answers to substitution map questions in special cases

Generalization of results in p-adic Hodge theory

Connections to p-adic dynamical systems

Abstract

We ask several questions about substitution maps in the Robba ring. These questions are motivated by $p$-adic Hodge theory and the theory of $p$-adic dynamical systems. We provide answers to those questions in special cases, thereby generalizing results of Kedlaya, Colmez, and others.