Minimality of $5$-adic polynomial dynamical systems

TL;DR

This paper characterizes 5-adic polynomial dynamical systems that have exactly one minimal component, providing insights into their structure and behavior within p-adic dynamics.

Contribution

It offers a complete characterization of minimal polynomial dynamical systems over 5-adic integers, a specific case in p-adic dynamics.

Findings

Identifies conditions for minimality in 5-adic polynomial systems

Provides a classification of systems with a single minimal component

Enhances understanding of p-adic dynamical behavior

Abstract

We characterize the dynamical systems consisting of the set of 5-adic integers and polynomial maps which consist of only one minimal component.