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Sibirskii Matematicheskii Zhurnal, 2021, Volume 62, Number 4, Pages 715–720
DOI: https://doi.org/10.33048/smzh.2021.62.401 (Mi smj7589) 		 
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
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DOI: https://doi.org/10.33048/smzh.2021.62.401
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.
Funding agency Grant number
Russian Science Foundation 19-11-00044
The first author was supported by the Russian Science Foundation (Grant 19–11–00044).
Received: 16.04.2021
Revised: 16.04.2021
Accepted: 11.06.2021
English version:
Siberian Mathematical Journal, 2021, Volume 62, Issue 4, Pages 581–585
DOI: https://doi.org/10.1134/S0037446621040017
Bibliographic databases:
Document Type: Article
UDC: 517.938
Language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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