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

Abstract

Let $K$ be a finite extension of the field $\mathbb{Q}_p$ of $p$-adic numbers and $Ø$ be its integral ring. The convergent power series with coefficients in $Ø$ are studied as dynamical systems on $Ø$. 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.

18pages