Proceedings of the Steklov Institute of Mathematics

, Volume 295, Issue 1, pp 225–242 | Cite as

On first integrals of geodesic flows on a two-torus

  • I. A. TaimanovEmail author


For a geodesic (or magnetic geodesic) flow, the problem of the existence of an additional (independent of the energy) first integral that is polynomial in momenta is studied. The relation of this problem to the existence of nontrivial solutions of stationary dispersionless limits of two-dimensional soliton equations is demonstrated. The nonexistence of an additional quadratic first integral is established for certain classes of magnetic geodesic flows.


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© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsSiberian Branch of the Russian Academy of SciencesNovosibirskRussia
  2. 2.Faculty of Mechanics and MathematicsNovosibirsk State UniversityNovosibirskRussia

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