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Mat. Sb., 2000, Volume 191, Number 2, Pages 3–42 (Mi msb451)  

This article is cited in 41 scientific papers (total in 42 papers)

The method of loop molecules and the topology of the Kovalevskaya top

A. V. Bolsinova, P. H. Richterb, A. T. Fomenko

a M. V. Lomonosov Moscow State University
b University of Bremen, Institute for Theoretical Physics

Abstract: A method for calculating topological invariants of the foliation of a phase space into invariant Liouville tori in the case of integrable Hamiltonian systems with two degrees of freedom is put forward. The structure of this foliation is completely described for the Kovalevskaya integrable case in rigid body dynamics.

DOI: https://doi.org/10.4213/sm451

Full text: PDF file (758 kB)
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English version:
Sbornik: Mathematics, 2000, 191:2, 151–188

Bibliographic databases:

Document Type: Article
UDC: 513.944+515.1
MSC: 58F07, 70E15
Received: 28.10.1999

Citation: A. V. Bolsinov, P. H. Richter, A. T. Fomenko, “The method of loop molecules and the topology of the Kovalevskaya top”, Mat. Sb., 191:2 (2000), 3–42; Sb. Math., 191:2 (2000), 151–188

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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:
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    5. P. E. Ryabov, “Bifurcations of First Integrals in the Sokolov Case”, Theoret. and Math. Phys., 134:2 (2003), 181–197  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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    31. M. P. Kharlamov, P. E. Ryabov, “Topological atlas of the Kovalevskaya top in a double field”, J. Math. Sci., 223:6 (2017), 775–809  mathnet  crossref  mathscinet  elib
    32. 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
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    37. V. A. Kibkalo, “The topology of the analog of Kovalevskaya integrability case on the Lie algebra $\mathrm{so}(4)$ under zero area integral”, Moscow University Mathematics Bulletin, 71:3 (2016), 119–123  mathnet  crossref  mathscinet  isi
    38. El-Sabaa F.M. Hosny M. Zakria S.K., “Bifurcations of Liouville Tori of a Two Fixed Center Problem”, Astrophys. Space Sci., 363:4 (2018), 77  crossref  mathscinet  isi  scopus  scopus  scopus
    39. Bolsinov A., Guglielmi L., Kudryavtseva E., “Symplectic Invariants For Parabolic Orbits and Cusp Singularities of Integrable Systems”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 376:2131 (2018), 20170424  crossref  isi  scopus
    40. V. V. Vedyushkina, I. S. Kharcheva, “Billiard books model all three-dimensional bifurcations of integrable Hamiltonian systems”, Sb. Math., 209:12 (2018), 1690–1727  mathnet  crossref  crossref  adsnasa  isi  elib
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    42. V. A. Kibkalo, “Topologicheskaya klassifikatsiya sloenii Liuvillya dlya integriruemogo sluchaya Kovalevskoi na algebre Li $\operatorname{so}(4)$”, Matem. sb., 210:5 (2019), 3–40  mathnet  crossref  elib
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