On the numerical computation of Diophantine rotation numbers of analytic circle maps

In this paper we present a numerical method to compute Diophantine rotation numbers of circle maps with high accuracy. We mainly focus on analytic circle diffeomorphisms, but the method also works in the case of (enough) finite differentiability. The keystone of the method is that, under these conditions, the map is conjugate to a rigid rotation of the circle. Moreover, although it is not fully justified by our construction, the method turns out to be quite efficient for computing rational rotation numbers. We discuss the method through several numerical examples.