The universal minimal one parameter system with quasi-discrete spectrum

Abstract

The universal minimal one parameter system will be characterized as the space $\Gamma ^{\infty }$, in which $\Gamma$ is the Bohr compactification of the additive group ${\mathbb {R}}$ of real numbers. In this way, we need to show that $\Gamma ^\infty$ is isomorphic to the spectrum of $W({\mathbb {R}})$, the norm closure of the invariant algebra generated by the maps $\exp q(t)$, where q(t) is a real polynomial on ${\mathbb {R}}$.