Circularly ordered dynamical systems

TL;DR

This paper investigates the topological properties of circularly ordered dynamical systems, demonstrating their representability on Rosenthal Banach spaces and exploring implications for topological groups and symbolic systems.

Contribution

It proves that all circularly ordered dynamical systems are representable on Rosenthal Banach spaces and characterizes circularly ordered minimal cascades, extending understanding of their structure.

Findings

Every circularly ordered dynamical system is representable on a Rosenthal Banach space.

Several Sturmian-like symbolic $\\mathbb{Z}^k$-systems are circularly ordered.

Circularly ordered minimal cascades are characterized using existing results.

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.