Dynamic Structures of Monomials on $p$-adic Integers for Small Primes $p$

TL;DR

This paper explores the dynamic behavior of monomials over $p$-adic integers for small primes, analyzing minimal decompositions into subsystems and basins to understand their structure.

Contribution

It provides a detailed description of the dynamic structures of monomials on $p$-adic integers specifically for primes 2, 3, and 5, including minimal decompositions.

Findings

Characterization of minimal subsystems and attracting basins for $p$-adic monomials

Explicit descriptions of dynamic structures for primes 2, 3, and 5

Insights into the decomposition of $p$-adic dynamical systems

Abstract

We study the dynamic structures of the monomial $x^m$ over the ring of $p$-adic integers for every positive integer $m$ and for primes $p=2,3$ and $5$. The dynamic structures are described by investigating minimal decompositions which consist of minimal subsystems and attracting basins.