An orbital classication of linearly and quadratically integrable geodesic ows

on the torus was obtained by E. N. Selivanova [312].

As was shown in Chapters 5 and 8, for orbital classication of integrable

systems, rst of all, it is necessary to calculate the rotation function on the edges

of the marked molecule W

. Consider a torus with an integrable geodesic ow.

We restrict ourselves to the case of a global Liouville metric.