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Эта публикация цитируется в 5 научных статьях (всего в 5 статьях)
The Topology of Liouville Foliation for the Borisov–Mamaev–Sokolov Integrable Case on the Lie Algebra $so(4)$
Rasoul Akbarzadeh, Ghorbanali Haghighatdoost
Azarbaijan Shahid Madani University, 35 Km Tabriz-Maragheh Road, Tabriz, Iran
Аннотация:
In 2001, A.V. Borisov, I.S. Mamaev, and V.V. Sokolov discovered a new integrable case on the Lie algebra $so(4)$. This system coincides with the Poincaré equations on the Lie algebra $so(4)$, which describe the motion of a body with cavities filled with an incompressible vortex fluid. Moreover, the Poincaré equations describe the motion of a four-dimensional gyroscope. In this paper topological properties of this system are studied. In particular, for the system under consideration the bifurcation diagrams of the momentum mapping are constructed and all Fomenko invariants are calculated. Thereby, a classification of isoenergy surfaces for this system up to the rough Liouville equivalence is obtained.
Ключевые слова:
integrable Hamiltonian systems, isoenergy surfaces, Kirchhoff equations, Liouville foliation, bifurcation diagram, Borisov–Mamaev–Sokolov case, topological invariant
DOI:
https://doi.org/10.1134/S1560354715030089
 Список литературы:
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Тип публикации:
Статья
MSC: 37J35, 70H06
Поступила в редакцию: 06.03.2015
Язык публикации: английский
Образец цитирования:
Rasoul Akbarzadeh, Ghorbanali Haghighatdoost, “The Topology of Liouville Foliation for the Borisov–Mamaev–Sokolov Integrable Case on the Lie Algebra $so(4)$”, Regul. Chaotic Dyn., 20:3 (2015), 317–344
Цитирование в формате AMSBIB
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\paper The Topology of Liouville Foliation for the Borisov–Mamaev–Sokolov Integrable Case on the Lie Algebra $so(4)$
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 3
\pages 317--344
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Образцы ссылок на эту страницу:
http://mi.mathnet.ru/rcd46 http://mi.mathnet.ru/rus/rcd/v20/i3/p317
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
Эта публикация цитируется в следующих статьяx:
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Rasoul Akbarzadeh, “Topological Analysis Corresponding to the Borisov–Mamaev–Sokolov Integrable System on the Lie Algebra $so(4)$”, Regul. Chaotic Dyn., 21:1 (2016), 1–17
 -
Pavel E. Ryabov, Andrej A. Oshemkov, Sergei V. Sokolov, “The Integrable Case of Adler – van Moerbeke. Discriminant Set and Bifurcation Diagram”, Regul. Chaotic Dyn., 21:5 (2016), 581–592
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A. A. Oshemkov, P. E. Ryabov, S. V. Sokolov, “Explicit determination of certain periodic motions of a generalized two-field gyrostat”, Russ. J. Math. Phys., 24:4 (2017), 517–525
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П. Е. Рябов, “Явное интегрирование системы инвариантных соотношений для случая М. Адлера и П. ван Мëрбеке”, Докл. РАН, 472:2 (2017), 130–134
 ; P. E. Ryabov, “Explicit integration of the system of invariant relations for the case of M. Adler and P. van Moerbeke”, Dokl. Math., 95:1 (2017), 17–20 -
Р. Акбарзаде, “Топология изоэнергетических поверхностей интегрируемого случая Борисова–Мамаева–Соколова на алгебре Ли $so(3,1)$”, ТМФ, 197:3 (2018), 385–396 ; R. Akbarzadeh, “The topology of isoenergetic surfaces for the Borisov–Mamaev–Sokolov integrable case on the Lie algebra $so(3,1)$”, Theoret. and Math. Phys., 197:3 (2018), 1727–1736
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