A non-archimedean Montel's theorem

TL;DR

This paper extends Montel's theorem to non-archimedean fields, defining normal families and exploring their implications for non-archimedean entire function dynamics.

Contribution

It introduces a non-archimedean version of Montel's theorem and a new definition of normal families in this setting.

Findings

Established a non-archimedean Montel's theorem

Proposed a definition of normal families in non-archimedean analysis

Applied results to non-archimedean entire function dynamics

Abstract

We prove a version of Montel's theorem for analytic functions over a non-archimedean complete valued field. We propose a definition of normal family in this context, and give applications of our results to the dynamics of non-archimedean entire functions.