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Izv. Akad. Nauk SSSR Ser. Mat., 1983, Volume 47, Issue 6, Pages 1248–1262 (Mi izv1462)  

This article is cited in 7 scientific papers (total in 7 papers)

Homogeneous spaces with integrable $G$-invariant Hamiltonian flows

I. V. Mykytyuk


Abstract: Examples are constructed of homogeneous spaces $M$ with semisimple groups of motions $G$ for which all $G$-invariant Hamiltonian systems on $T^*M$ are integrable. Particular examples of such include affine symmetric spaces.
Bibliography: 11 titles.

Full text: PDF file (1463 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1984, 23:3, 511–523

Bibliographic databases:

UDC: 519.46
MSC: Primary 58F07; Secondary 58F05, 70H99, 34C35, 22E60
Received: 05.10.1982

Citation: I. V. Mykytyuk, “Homogeneous spaces with integrable $G$-invariant Hamiltonian flows”, Izv. Akad. Nauk SSSR Ser. Mat., 47:6 (1983), 1248–1262; Math. USSR-Izv., 23:3 (1984), 511–523

Citation in format AMSBIB
\Bibitem{Myk83}
\by I.~V.~Mykytyuk
\paper Homogeneous spaces with integrable $G$-invariant Hamiltonian flows
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1983
\vol 47
\issue 6
\pages 1248--1262
\mathnet{http://mi.mathnet.ru/izv1462}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=727754}
\zmath{https://zbmath.org/?q=an:0554.58030|0539.58016}
\transl
\jour Math. USSR-Izv.
\yr 1984
\vol 23
\issue 3
\pages 511--523
\crossref{https://doi.org/10.1070/IM1984v023n03ABEH001783}


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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. I. V. Mykytyuk, “Integrability of the Euler equations associated with filtrations of semisimple Lie algebras”, Math. USSR-Sb., 53:2 (1986), 541–549  mathnet  crossref  mathscinet  zmath
    2. I. V. Mykytyuk, “On the integrability of invariant Hamiltonian systems with homogeneous configuration spaces”, Math. USSR-Sb., 57:2 (1987), 527–546  mathnet  crossref  mathscinet  zmath
    3. A. V. Brailov, “Construction of completely integrable geodesic flows on compact symmetric spaces”, Math. USSR-Izv., 29:1 (1987), 19–31  mathnet  crossref  mathscinet  zmath
    4. M. L. Chumak, “Integrable $G$-invariant Hamiltonian systems and homogeneous spaces with simple spectrum”, Funct. Anal. Appl., 20:4 (1986), 334–336  mathnet  crossref  mathscinet  zmath  isi
    5. A. V. Bolsinov, B. Jovanović, “Integrable geodesic flows on homogeneous spaces”, Sb. Math., 192:7 (2001), 951–968  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. A. A. Magazev, I. V. Shirokov, “Integration of Geodesic Flows on Homogeneous Spaces: The Case of a Wild Lie Group”, Theoret. and Math. Phys., 136:3 (2003), 1212–1224  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. Bolsinov A.V., “Integrable geodesic flows on Riemannian manifolds: Construction and obstructions”, Proceedings of the Workshop on Contemporary Geometry and Related Topics, 2004, 57–103  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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