Isolated circular orders of PSL(2,Z)

TL;DR

This paper establishes a correspondence between isolated circular orders of PSL(2,Z) and Markov systems, providing new examples of such orders and advancing understanding of their structure.

Contribution

It introduces a bijection linking isolated circular orders of PSL(2,Z) to Markov systems, offering a novel framework and explicit examples.

Findings

Established a bijection between isolated circular orders and Markov systems.

Provided explicit examples of isolated circular orders of PSL(2,Z).

Enhanced understanding of the structure of circular orders in PSL(2,Z).

Abstract

We give a bijection between the isolated circular orders of the group G=PSL(2,Z) and the equivalence classes of Markov systems associated with G. As applications, we present examples of isolated circular order of G.