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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:
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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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\pages 180--196
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http://mi.mathnet.ru/eng/rcd250 http://mi.mathnet.ru/eng/rcd/v22/i2/p180
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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
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