Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space |
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| Authors: | V N Ushakov P D Lebedev |
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| Institution: | 1.Sobolev Institute of Mathematics,Siberian Branch of the Russian Academy of Sciences,Novosibirsk,Russia;2.Faculty of Mechanics and Mathematics,Novosibirsk State University,Novosibirsk,Russia |
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| Abstract: | 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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