Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2017, Volume 13, Number 3, Pages 433–452
DOI: https://doi.org/10.20537/nd1703010
(Mi nd576)
 

This article is cited in 8 scientific papers (total in 8 papers)

Translated papers

The Hess–Appelrot case and quantization of the rotation number

I. A. Bizyaev, A. V. Borisov, I. S. Mamaev

Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Full-text PDF (545 kB) Citations (8)
References:
Abstract: This paper is concerned with the Hess case in the Euler–Poisson equations and with its generalization on the pencil of Poisson brackets. It is shown that in this case the problem reduces to investigating the vector field on a torus and that the graph showing the dependence of the rotation number on parameters has horizontal segments (limit cycles) only for integer values of the rotation number. In addition, an example of a Hamiltonian system is given which possesses an invariant submanifold (similar to the Hess case), but on which the dependence of the rotation number on parameters is a Cantor ladder.
Keywords: invariant submanifold, rotation number, Cantor ladder, limit cycles.
Funding agency Grant number
Russian Science Foundation 14-50-00005
Received: 02.02.2017
Accepted: 06.03.2017
English version:
Regular and Chaotic Dynamics, 2017, Volume 22, Issue 2, Pages 180–196
DOI: https://doi.org/10.1134/S156035471702006X
Bibliographic databases:
Document Type: Article
UDC: 517.925
MSC: 70E17, 37E45
Language: Russian
Citation: I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “The Hess–Appelrot case and quantization of the rotation number”, Nelin. Dinam., 13:3 (2017), 433–452; Regular and Chaotic Dynamics, 22:2 (2017), 180–196
Citation in format AMSBIB
\Bibitem{BizBorMam17}
\by I.~A.~Bizyaev, A.~V.~Borisov, I.~S.~Mamaev
\paper The Hess–Appelrot case and quantization of the rotation number
\jour Nelin. Dinam.
\yr 2017
\vol 13
\issue 3
\pages 433--452
\mathnet{http://mi.mathnet.ru/nd576}
\crossref{https://doi.org/10.20537/nd1703010}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3658423}
\elib{https://elibrary.ru/item.asp?id=29993271}
\transl
\jour Regular and Chaotic Dynamics
\yr 2017
\vol 22
\issue 2
\pages 180--196
\crossref{https://doi.org/10.1134/S156035471702006X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85031088531}
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  • https://www.mathnet.ru/eng/nd/v13/i3/p433
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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