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Sibirskii Matematicheskii Zhurnal, 2023, Volume 64, Number 2, Pages 243–251
DOI: https://doi.org/10.33048/smzh.2023.64.201 (Mi smj7758) 		 
This article is cited in 2 scientific papers (total in 2 papers)

High-degree polynomial integrals of a natural system on the two-dimensional torus

S. V. Agapovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Full-text PDF (300 kB) Citations (2)
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DOI: https://doi.org/10.33048/smzh.2023.64.201
Abstract: We study a natural mechanical system on the two-dimensional torus which admits an additional first integral polynomial in momenta of an odd degree NN and independent of the energy integral. For N=5,7N=5,7, we obtain the estimates on the number of straight lines in the spectrum of the potential.
Keywords: natural mechanical system, first integral polynomial in momenta, spectrum of the potential.
Funding agency Grant number
Russian Science Foundation 19-11-00044-П
The author was supported by the Russian Science Foundation (Grant no. 19–11–00044–P).
Received: 13.07.2022
Revised: 25.07.2022
Accepted: 15.08.2022
English version:
Siberian Mathematical Journal, 2023, Volume 64, Issue 2, Pages 261–268
DOI: https://doi.org/10.1134/S0037446623020015
Bibliographic databases:
Document Type: Article
UDC: 517.938
Language: Russian
Citation: S. V. Agapov, “High-degree polynomial integrals of a natural system on the two-dimensional torus”, Sibirsk. Mat. Zh., 64:2 (2023), 243–251; Siberian Math. J., 64:2 (2023), 261–268
Citation in format AMSBIB
\Bibitem{Aga23}
\by S.~V.~Agapov
\paper High-degree polynomial integrals of a~natural system on the two-dimensional torus
\jour Sibirsk. Mat. Zh.
\yr 2023
\vol 64
\issue 2
\pages 243--251
\mathnet{http://mi.mathnet.ru/smj7758}
\crossref{https://doi.org/10.33048/smzh.2023.64.201}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4567661}
\transl
\jour Siberian Math. J.
\yr 2023
\vol 64
\issue 2
\pages 261--268
\crossref{https://doi.org/10.1134/S0037446623020015}
Linking options:
  • https://www.mathnet.ru/eng/smj7758
  • https://www.mathnet.ru/eng/smj/v64/i2/p243
    • This publication is cited in the following 2 articles:
    1. S. V. Agapov, M. M. Tursunov, “O ratsionalnykh integralakh dvumernykh naturalnykh sistem”, Sib. matem. zhurn., 64:4 (2023), 665–674  mathnet  crossref
    2. S. V. Agapov, M. M. Tursunov, “On the Rational Integrals of Two-Dimensional Natural Systems”, Sib Math J, 64:4 (2023), 787  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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