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arXiv · 1610.04822

On first integrals of geodesic flows on a two-torus

I. A. Taimanov
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Abstract

The problem of the existence of an additional (independent on the energy) first integral, of a geodesic (or magnetic geodesic) flow, which 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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I. A. Taimanov. 2016-10-16. On first integrals of geodesic flows on a two-torus. https://arxiv.org/abs/1610.04822

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