Fractional-linear integrals of geodesic flows on surfaces and Nakai's geodesic 4-webs

Sergey I. Agafonov, Thaís G. P. Alves

We prove that if the geodesic flow on a surface has an integral, fractional-linear in momenta, then the dimension of the space of such integrals is either 3 or 5, the latter case c…