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Uspekhi Mat. Nauk, 1990, Volume 45, Issue 6(276), Pages 91–111 (Mi umn4807)  

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

Topological classification of integrable non-degenerate Hamiltonians on a constant energy three-dimensional sphere

Nguyen Tien Zung, A. T. Fomenko

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Full text: PDF file (1374 kB)
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English version:
Russian Mathematical Surveys, 1990, 45:6, 109–135

Bibliographic databases:

Document Type: Article
UDC: 513.944
MSC: 70H06, 70G40, 70K42
Received: 20.07.1990

Citation: Nguyen Tien Zung, A. T. Fomenko, “Topological classification of integrable non-degenerate Hamiltonians on a constant energy three-dimensional sphere”, Uspekhi Mat. Nauk, 45:6(276) (1990), 91–111; Russian Math. Surveys, 45:6 (1990), 109–135

Citation in format AMSBIB
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\paper Topological classification of integrable non-degenerate Hamiltonians on a~constant energy three-dimensional sphere
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\pages 91--111
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\transl
\jour Russian Math. Surveys
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\vol 45
\issue 6
\pages 109--135
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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. V. V. Kalashnikov, “Geometric description of minimax Fomenko invariants of integrable Hamiltonian systems on $S^3$, $RP^3$, $S^1 \times S^2$$T^3$”, Russian Math. Surveys, 46:4 (1991), 177–178  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Nguyen Tien Zung, “The complexity of integrable Hamiltonian systems on a prescribed three-dimensional constant-energy submanifold”, Russian Acad. Sci. Sb. Math., 75:2 (1993), 507–533  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Nguyen Tien Zung, L. S. Polyakova, E. N. Selivanova, “Topological Classification of Integrable Geodesic Flows on Orientable Two-Dimensional Riemannian Manifolds with Additional Integral Depending on Momenta Linearly or Quadratically”, Funct. Anal. Appl., 27:3 (1993), 186–196  mathnet  crossref  mathscinet  zmath  isi
    4. K. N. Mishachev, “Hamiltonian links in three-dimensional manifolds”, Izv. Math., 59:6 (1995), 1193–1205  mathnet  crossref  mathscinet  zmath  isi
    5. B. Campos, P. Vindel, “Graphs of NMS Flows on S 3 with Knotted Saddle Orbits and No Heteroclinic Trajectories”, Acta Math Sinica, 23:12 (2007), 2213  crossref  mathscinet  zmath  isi
    6. O. A. Zagryadskii, E. A. Kudryavtseva, D. A. Fedoseev, “A generalization of Bertrand's theorem to surfaces of revolution”, Sb. Math., 203:8 (2012), 1112–1150  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. N. S. Slavina, “Topological classification of systems of Kovalevskaya-Yehia type”, Sb. Math., 205:1 (2014), 101–155  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. S. S. Nikolaenko, “A topological classification of the Chaplygin systems in the dynamics of a rigid body in a fluid”, Sb. Math., 205:2 (2014), 224–268  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. E. A. Kudryavtseva, D. A. Fedoseev, “Mechanical systems with closed orbits on manifolds of revolution”, Sb. Math., 206:5 (2015), 718–737  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. I. V. Sypchenko, D. S. Timonina, “Closed geodesics on piecewise smooth surfaces of revolution with constant curvature”, Sb. Math., 206:5 (2015), 738–769  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. D. A. Fedoseev, A. T. Fomenko, “Nekompaktnye osobennosti integriruemykh dinamicheskikh sistem”, Fundament. i prikl. matem., 21:6 (2016), 217–243  mathnet
    12. E. A. Kudryavtseva, D. A. Fedoseev, “The Bertrand's manifolds with equators”, Moscow University Mathematics Bulletin, 71:1 (2016), 23–26  mathnet  crossref  mathscinet  isi
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