Dynamics of the $a$-map over residually finite Dedekind Domains and applications

Abstract

Let $\mathfrak{D}$ be a residually finite Dedekind domain, $a\in \mathfrak{D}$ be a nonzero element and $\mathfrak{n}$ be a nonzero ideal of $\mathfrak{D}$. In this paper we describe the dynamics of the map $x\mapsto ax$ over the quotient ring $\mathfrak{D}/\mathfrak{n}$. We further present some applications of our main result.

15 pages; comments welcome