My knowledge in many mathematics topics is far from completeness, so please consider my question as so-called soft question.
I know that Viroso group is a central extension of group of circle diffeomorphism group $\text{Diff}_{+}(S^1)$. Next, there is an object in theory of circle maps, which is called Arnold tongue. To develop intuition about the Arnold tongues, we can consider the very simple map,$$\theta_{n+1} = \theta_{n} + \omega + \frac{K}{2\pi}\sin\theta_n$$and define the rotation number as $\rho=\lim\limits_{n\rightarrow\infty}\theta_n/n$.
Question: how should I interpret the rotation number $\rho$ in terms of Virasoro group?