Dynamics of convergent power series on the integral ring of a finite extension of $\text{Qp}$

Let $K$ be a finite extension of the field ${\mathbb{Q}}_p$ of $p$-adic numbers and $\text{O}$ be its integral ring. The convergent power series with coefficients in $\text{O}$ are studied as dynamical systems on $\text{O}$. A minimal decomposition theorem for such a dynamical system is obtained. It is proved that there are uncountably many minimal subsystems, provided that there is a minimal set consisting of infinitely many points. In particular, the complete detailed minimal decompositions of all affine systems are derived.