Cubic and quartic integrals for geodesic flow on 2-torus via a system of the hydrodynamic type
Cubic and quartic integrals for geodesic flow on 2-torus via a system of the hydrodynamic type
In this paper, we deal with the classical question of the existence of polynomials in momenta integrals for geodesic flows on the 2-torus. For the quasilinear system on the coefficients of the polynomial integral, we investigate the region (so-called elliptic region) where two of the eigenvalues are complex conjugate. We …