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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 4, Pages 721–734
DOI: https://doi.org/10.33048/smzh.2020.61.401 (Mi smj6015) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On first integrals of two-dimensional geodesic flows

S. V. Agapovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Full-text PDF (434 kB) Citations (5)
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DOI: https://doi.org/10.33048/smzh.2020.61.401
Abstract: We study the first integrals polynomial and rational in momenta of the geodesic flows (including those in a magnetic field) on two-dimensional surfaces.
Keywords: geodesic flow, first integral, magnetic field.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.Y26.31.0025
Russian Foundation for Basic Research 18-01-00411_а
SectionsВ 2 andВ 4 were supported by the Laboratory of Topology and Dynamics of Novosibirsk State University (Contract no.В 14.Y26.31.0025 with the Ministry of Education and Science of the Russian Federation). SectionВ 3 was supported by the RFBR GrantВ 18–01–00411 “Nonlinear Systems and Geometry.”
Received: 10.01.2020
Revised: 02.06.2020
Accepted: 17.06.2020
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 4, Pages 563–574
DOI: https://doi.org/10.1134/S0037446620040011
Bibliographic databases:
Document Type: Article
UDC: 517.938
MSC: 35R30
Language: Russian
Citation: S. V. Agapov, “On first integrals of two-dimensional geodesic flows”, Sibirsk. Mat. Zh., 61:4 (2020), 721–734; Siberian Math. J., 61:4 (2020), 563–574
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/smj6015
  • https://www.mathnet.ru/eng/smj/v61/i4/p721
    • This publication is cited in the following 5 articles:
    1. Sergei Agapov, Vladislav Shubin, “New examples of non-polynomial integrals of two-dimensional geodesic flows *”, J. Phys. A: Math. Theor., 57:1 (2024), 015204  crossref
    2. Sergey I. Agafonov, Thaís G. P. Alves, “Fractional-linear integrals of geodesic flows on surfaces and Nakai's geodesic 4-webs”, Advances in Geometry, 24:2 (2024), 263  crossref
    3. Sergei Agapov, Alexey Potashnikov, Vladislav Shubin, “Integrable magnetic geodesic flows on 2-surfaces *”, Nonlinearity, 36:4 (2023), 2128  crossref
    4. 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”, Siberian Math. J., 62:4 (2021), 581–585  mathnet  crossref  crossref  isi  elib
    5. S. Agapov, V. Shubin, “Rational integrals of 2-dimensional geodesic flows: new examples”, J. Geom. Phys., 170 (2021), 104389  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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