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Nelin. Dinam., 2017, Volume 13, Number 3, Pages 433–452 (Mi nd576)  

Translated papers

The HessAppelrot 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

Abstract: This paper is concerned with the Hess case in the EulerPoisson 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


DOI: https://doi.org/10.20537/nd1703010

Full text: PDF file (545 kB)
References: PDF file   HTML file

English version:
Regular and Chaotic Dynamics, 2017, 22:2, 180–196

Bibliographic databases:

Document Type: Article
UDC: 517.925
MSC: 70E17, 37E45
Received: 02.02.2017

Citation: I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “The HessAppelrot 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 HessAppelrot 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://www.ams.org/mathscinet-getitem?mr=3658423}
\elib{http://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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85016971181}


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