Circularly ordered dynamical systems

Abstract

We study topological properties of circularly ordered dynamical systems and prove that every such system is representable on a Rosenthal Banach space, hence, is also tame. We derive some consequences for topological groups. We show that several Sturmian like symbolic $\mathbb{Z}^k$-systems are circularly ordered. Using some old results we characterize circularly ordered minimal cascades.