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arXiv · 2205.12499

Integrable magnetic geodesic flows on 2-surfaces

Sergei Agapov·Alexey Potashnikov·Vladislav Shubin
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Abstract

We study the magnetic geodesic flows on 2-surfaces having an additional first integral which is independent of the Hamiltonian at a fixed energy level. The following two cases are considered: when there exists a quadratic in momenta integral, and also the case of a rational in momenta integral with a linear numerator and denominator. In both cases certain semi-Hamiltonian systems of PDEs appear. In this paper we construct exact solutions (generally speaking, local ones) to these systems: in the first case via the generalized hodograph method, in the second case via the Legendre transformation and the method of separation of variables.

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Sergei Agapov, Alexey Potashnikov, Vladislav Shubin. 2022-05-25. Integrable magnetic geodesic flows on 2-surfaces. https://doi.org/10.1088/1361-6544/acc0c5

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