Sibirskii Matematicheskii Zhurnal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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
Full-text PDF (364 kB) Citations (1)
References:
PDF
HTML
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
\Bibitem{AgaValShu21}
\by S.~V.~Agapov, A.~A.~Valyuzhenich, V.~V.~Shubin
\paper Some remarks on~high degree polynomial integrals of the magnetic geodesic flow on the two-dimensional torus
\jour Sibirsk. Mat. Zh.
\yr 2021
\vol 62
\issue 4
\pages 715--720
\mathnet{http://mi.mathnet.ru/smj7589}
\crossref{https://doi.org/10.33048/smzh.2021.62.401}
\elib{https://elibrary.ru/item.asp?id=47036040}
\transl
\jour Siberian Math. J.
\yr 2021
\vol 62
\issue 4
\pages 581--585
\crossref{https://doi.org/10.1134/S0037446621040017}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000682525600001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85112650914}
Linking options:
  • https://www.mathnet.ru/eng/smj7589
  • https://www.mathnet.ru/eng/smj/v62/i4/p715
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
    Statistics & downloads:
    Abstract page:211
    Full-text PDF :29
    References:42
    First page:12
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024