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

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.