Minimal Dynamical System for $\mathbb{R}^n$

Abstract

We investigate $\mathbb{R}^n$ as the additive group with the Euclidean topology to give a description of $S(\mathbb{R}^n)$, the phase space of the universal ambit of $\mathbb{R}^n$ and $M(\mathbb{R}^n)$, the phase space of the universal minimal dynamical system, in terms of $M(\mathbb{Z}^n)$, the phase space of universal minimal flow of $\mathbb{Z}^n$. This extends work by Turek for $\mathbb{R}$ to $\mathbb{R}^n$.