Minimal polynomial dynamics on the set of 3-adic integers

TL;DR

This paper characterizes polynomials over the 3-adic integers that have dense orbits, providing a detailed description of their coefficients.

Contribution

It offers a complete characterization of polynomials with dense orbits in the 3-adic integers based on their coefficients.

Findings

Identifies conditions on polynomial coefficients for dense orbits

Provides a classification of such polynomials in the 3-adic setting

Enhances understanding of polynomial dynamics in p-adic systems

Abstract

In this paper are characterized the polynomials, in terms of their coefficients, that have all their orbits dense in the set of 3-adic integers.