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Regul. Chaotic Dyn., 2017, Volume 22, Issue 2, Pages 180–196 (Mi rcd250)  

This article is cited in 1 scientific paper (total in 1 paper)

The Hess–Appelrot Case and Quantization of the Rotation Number

Ivan A. Bizyaev, Alexey V. Borisov, Ivan 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 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
This work was supported by the Russian Science Foundation (project 14-50-00005).


DOI: https://doi.org/10.1134/S156035471702006X

References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 70E17, 37E45
Received: 02.02.2017
Language: English

Citation: Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Hess–Appelrot Case and Quantization of the Rotation Number”, Regul. Chaotic Dyn., 22:2 (2017), 180–196

Citation in format AMSBIB
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\by Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev
\paper The Hess–Appelrot Case and Quantization of the Rotation Number
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 2
\pages 180--196
\mathnet{http://mi.mathnet.ru/rcd250}
\crossref{https://doi.org/10.1134/S156035471702006X}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3631898}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Ol'shanskii V.Yu., “Partial Linear Integrals of the Poincaré-Zhukovskii Equations (the General Case)”, Pmm-J. Appl. Math. Mech., 81:4 (2017), 270–285  crossref  mathscinet  isi  scopus
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