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Mat. Sb. (N.S.), 1981, Volume 115(157), Number 2(6), Pages 263–280 (Mi msb2384)  

This article is cited in 13 scientific papers (total in 13 papers)

On symplectic structures and integrable systems on symmetric spaces

A. T. Fomenko


Abstract: The paper is concerned with the construction and investigation of new classes of completely integrable Hamiltonian systems.
Figures: 5.
Bibliography: 7 titles.

Full text: PDF file (1911 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1982, 43:2, 235–250

Bibliographic databases:

UDC: 517.9+519.46
MSC: Primary 58F05, 53C15, 57C35; Secondary 58F25, 17B99, 34C35
Received: 07.04.1980

Citation: A. T. Fomenko, “On symplectic structures and integrable systems on symmetric spaces”, Mat. Sb. (N.S.), 115(157):2(6) (1981), 263–280; Math. USSR-Sb., 43:2 (1982), 235–250

Citation in format AMSBIB
\Bibitem{Fom81}
\by A.~T.~Fomenko
\paper On symplectic structures and integrable systems on symmetric spaces
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 115(157)
\issue 2(6)
\pages 263--280
\mathnet{http://mi.mathnet.ru/msb2384}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=622147}
\zmath{https://zbmath.org/?q=an:0488.58010|0467.58014}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 43
\issue 2
\pages 235--250
\crossref{https://doi.org/10.1070/SM1982v043n02ABEH002446}


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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. Trofimov V., “Completely Integrable Geodetic Flows of the Left-Invariant Metrics on Lie-Groups, Connected with Commutative Graduated Algebras with the Poincaré-Duality”, 263, no. 4, 1982, 812–816  mathscinet  zmath  isi
    2. Le Ngok T'euen, “Commutative collections of functions on orbits of finite-dimensional Lie algebras in general position”, Russian Math. Surveys, 38:1 (1983), 204–206  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. M. V. Meshcheryakov, “A characteristic property of the inertial tensor of a multidimensional solid body”, Russian Math. Surveys, 38:5 (1983), 156–157  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. V. V. Trofimov, A. T. Fomenko, “Dynamical systems on the orbits of linear representations of Lie groups and the complete integrability of certain hydrodynamical systems”, Funct. Anal. Appl., 17:1 (1983), 23–29  mathnet  crossref  mathscinet  zmath  isi
    5. V. V. Trofimov, A. T. Fomenko, “Liouville integrability of Hamiltonian systems on Lie algebras”, Russian Math. Surveys, 39:2 (1984), 1–67  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. Fomenko A., “Algebraic Properties of Some Integrable Hamiltonian-Systems”, 1060, 1984, 246–257  mathscinet  zmath  isi
    7. Trofimov V., “Symplectical Structures on Groups of Automorphisms of Symmetrical Spaces”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1984, no. 6, 31–33  mathscinet  zmath  isi
    8. È. B. Vinberg, “On certain commutative subalgebras of a universal enveloping algebra”, Math. USSR-Izv., 36:1 (1991), 1–22  mathnet  crossref  mathscinet  zmath  adsnasa
    9. Partha Guha, “Adler–Kostant–Symes construction, bi-Hamiltonian manifolds, and KdV equations”, J. Math. Phys, 38:10 (1997), 5167  crossref
    10. L. G. Rybnikov, “Centralizers of certain quadratic elements in Poisson–Lie algebras and the method of translation of invariants”, Russian Math. Surveys, 60:2 (2005), 367–369  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. Mouna F., Bouetou T.B., Nguiffo M.B., “On Cohomology of Nilpotent Symplectic Lie Algebras of Dim. <= 6 and Deformation of Those of Dim. <= 4”, Int. J. Geom. Methods Mod. Phys., 9:3 (2012), 1250020  crossref  mathscinet  isi
    12. I. K. Kozlov, “An Elementary Proof of the Jordan–Kronecker Theorem”, Math. Notes, 94:6 (2013), 885–896  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    13. A. Yu. Konyaev, “Classification of Lie algebras with generic orbits of dimension 2 in the coadjoint representation”, Sb. Math., 205:1 (2014), 45–62  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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