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Matematicheskie Zametki, 1998, Volume 64, Issue 1, Pages 37–44
DOI: https://doi.org/10.4213/mzm1370 (Mi mzm1370) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Integrals polynomial in velocity for two-degrees-of-freedom dynamical systems whose configuration space is a torus

N. V. Denisova

M. V. Lomonosov Moscow State University
Full-text PDF (184 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm1370
Abstract: We consider dynamical systems with two degrees of freedom whose configuration space is a torus and which admit first integrals polynomial in velocity. We obtain constructive criteria for the existence of conditional linear and quadratic integrals on the two-dimensional torus. Moreover, we show that under some additional conditions the degree of an “irreducible” integral of the geodesic flow on the torus does not exceed 2.
Received: 14.02.1997
Revised: 14.05.1997
English version:
Mathematical Notes, 1998, Volume 64, Issue 1, Pages 31–37
DOI: https://doi.org/10.1007/BF02307193
Bibliographic databases:
UDC: 517.9+531.01
Language: Russian
Citation: N. V. Denisova, “Integrals polynomial in velocity for two-degrees-of-freedom dynamical systems whose configuration space is a torus”, Mat. Zametki, 64:1 (1998), 37–44; Math. Notes, 64:1 (1998), 31–37
Citation in format AMSBIB
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\pages 37--44
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\transl
\jour Math. Notes
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\vol 64
\issue 1
\pages 31--37
\crossref{https://doi.org/10.1007/BF02307193}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000078147600005}
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  • https://www.mathnet.ru/eng/mzm1370
  • https://doi.org/10.4213/mzm1370
  • https://www.mathnet.ru/eng/mzm/v64/i1/p37
    • This publication is cited in the following 2 articles:
    1. Kozlov, VV, “Topological obstructions to the existence of quantum conservation laws”, Doklady Mathematics, 71:2 (2005), 300  mathnet  mathscinet  zmath  isi  elib
    2. N. V. Denisova, V. V. Kozlov, “Polynomial integrals of reversible mechanical systems with a two-dimensional torus as the configuration space”, Sb. Math., 191:2 (2000), 189–208  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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