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This article is cited in 1 scientific paper (total in 1 paper)
Some remarks on high degree polynomial integrals of the magnetic geodesic flow on the two-dimensional torus
S. V. Agapovab, A. A. Valyuzhenicha, V. V. Shubinb a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Abstract:
We study the magnetic geodesic flow on the two-dimensional torus which admits an additional high degree first integral polynomial in momenta and is independent of the energy integral. In an earlier work by the first two authors, it was announced that if such integral is preserved at a sufficiently many different energy levels then there necessarily exists a linear integral at all energy levels. The proof of the announce was incomplete. Here we finish the proof of the above assertion.
Keywords:
magnetic geodesic flow, polynomial first integral.
Received: 16.04.2021 Revised: 16.04.2021 Accepted: 11.06.2021
Citation:
S. V. Agapov, A. A. Valyuzhenich, V. V. Shubin, “Some remarks on high degree polynomial integrals of the magnetic geodesic flow on the two-dimensional torus”, Sibirsk. Mat. Zh., 62:4 (2021), 715–720; Siberian Math. J., 62:4 (2021), 581–585
Linking options:
https://www.mathnet.ru/eng/smj7589 https://www.mathnet.ru/eng/smj/v62/i4/p715
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Abstract page: | 234 | Full-text PDF : | 34 | References: | 54 | First page: | 12 |
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