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arXiv · 1812.01290

Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels

Sergey Agapov·Alexandr Valyuzhenich
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Abstract

In this paper the geodesic flow on a 2-torus in a non-zero magnetic field is considered. Suppose that this flow admits an additional first integral $F$ on $N+2$ different energy levels which is polynomial in momenta of arbitrary degree $N$ with analytic periodic coefficients. It is proved that in this case the magnetic field and metrics are functions of one variable and there exists a linear in momenta first integral on all energy levels.

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Sergey Agapov, Alexandr Valyuzhenich. 2018-12-04. Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels. https://arxiv.org/abs/1812.01290

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