We give a bijection between the isolated circular orders of the group $G=\operatorname{PSL}(2,\mathbb{Z})\approx (\mathbb{Z}/2\mathbb{Z})*(\mathbb{Z}/3\mathbb{Z})$ and the equivalence classes of Markov systems associated to $G$. As applications, we present examples of isolated circular orders of the group $G$.

中文翻译：

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PSL(2,$\mathbb{Z}$) 的孤立循环阶数

我们给出了群 $G=\operatorname{PSL}(2,\mathbb{Z})\approx (\mathbb{Z}/2\mathbb{Z})*(\mathbb{ Z}/3\mathbb{Z})$ 和与 $G$ 相关的马尔可夫系统的等价类。作为应用，我们展示了 $G$ 组的孤立循环订单的示例。