Power-free points in quadratic number fields: Stabiliser, dynamics and entropy

TL;DR

This paper explores the structure and dynamics of k-free integers in quadratic number fields, linking number theory with topological dynamics to understand symmetries and entropy.

Contribution

It establishes new correspondences between number-theoretic properties and dynamical systems, highlighting the role of symmetries and entropy in these contexts.

Findings

Identified symmetries affecting the dynamical systems

Connected number-theoretic and dynamical quantities

Used entropy to distinguish different systems

Abstract

The sets of $k$-free integers in general quadratic number fields are studied, with special emphasis on (extended) symmetries and their impact on the topological dynamical systems induced by such integers. We establish correspondences between number-theoretic and dynamical quantities, and use symmetries and entropy to distinguish the systems.