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TMF, 2003, Volume 134, Number 2, Pages 207–226 (Mi tmf154)  

This article is cited in 12 scientific papers (total in 12 papers)

Bifurcations of First Integrals in the Sokolov Case

P. E. Ryabov

Finance Academy under the Government of the Russian Federation

Abstract: We study the phase topology of a new Liouville integrable Hamiltonian system with an additional quartic integral (the Sokolov case).

Keywords: Kirchhoff equations, integrable Hamiltonian systems, bifurcations of the Liouville tori

DOI: https://doi.org/10.4213/tmf154

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English version:
Theoretical and Mathematical Physics, 2003, 134:2, 181–197

Bibliographic databases:

Received: 20.02.2002

Citation: P. E. Ryabov, “Bifurcations of First Integrals in the Sokolov Case”, TMF, 134:2 (2003), 207–226; Theoret. and Math. Phys., 134:2 (2003), 181–197

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. P. V. Morozov, “Topology of Liouville foliations in the Steklov and the Sokolov integrable cases of Kirchhoff's equations”, Sb. Math., 195:3 (2004), 369–412  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Fomenko A.T., Morozov P.V., “Some new results in topological classification of integrable systems in rigid body dynamics”, Proceedings of the Workshop on Contemporary Geometry and Related Topics, 2004, 201–222  crossref  mathscinet  zmath  isi
    3. Valentin D. Irtegov, Tatyana N. Titorenko, “On One Approach to Investigation of Mechanical Systems”, SIGMA, 2 (2006), 049, 20 pp.  mathnet  crossref  mathscinet  zmath
    4. Irtegov V., Titorenko T., “On the peculiar properties of families of invariant manifolds of conservative systems”, Computer Algebra in Scientific Computing, Proceedings, Lecture Notes in Computer Science, 4770, 2007, 195–210  crossref  zmath  isi
    5. D. V. Novikov, “Topological features of the Sokolov integrable case on the Lie algebra $\mathrm{e}(3)$”, Sb. Math., 202:5 (2011), 749–781  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. V. D. Irtegov, T. N. Titorenko, “Computer algebra methods in the study of nonlinear differential systems”, Comput. Math. Math. Phys., 53:6 (2013), 845–857  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. D. V. Novikov, “Topological features of the Sokolov integrable case on the Lie algebra $\mathrm{so}(3,1)$”, Sb. Math., 205:8 (2014), 1107–1132  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. P. E. Ryabov, A. Yu. Savushkin, “Fazovaya topologiya volchka Kovalevskoi – Sokolova”, Nelineinaya dinam., 11:2 (2015), 287–317  mathnet
    9. Rasoul Akbarzadeh, Ghorbanali Haghighatdoost, “The Topology of Liouville Foliation for the BorisovMamaevSokolov Integrable Case on the Lie Algebra $so(4)$”, Regul. Chaotic Dyn., 20:3 (2015), 317–344  mathnet  crossref  mathscinet  zmath  adsnasa
    10. Rasoul Akbarzadeh, “Topological Analysis Corresponding to the BorisovMamaevSokolov Integrable System on the Lie Algebra $so(4)$”, Regul. Chaotic Dyn., 21:1 (2016), 1–17  mathnet  crossref  mathscinet  zmath
    11. Mikhail P. Kharlamov, Pavel E. Ryabov, Alexander Yu. Savushkin, “Topological Atlas of the KowalevskiSokolov Top”, Regul. Chaotic Dyn., 21:1 (2016), 24–65  mathnet  crossref  mathscinet  zmath
    12. 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  mathnet  crossref  crossref  adsnasa  isi  elib
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