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 Mat. Sb. (N.S.), 1978, Volume 106(148), Number 2(6), Pages 154–161 (Mi msb2562)

Integrability of the Euler equations on homogeneous symplectic manifolds

Dào Trong Thi

Abstract: Any strictly homogeneous symplectic manifold $M$ with a group of motions $\mathscr G$ may be considered as an orbit of the coadjoint action of $\mathscr G$. Therefore all Hamiltonian systems defined on an orbit, in particular Euler's equations, are carried over to $M$ in a natural way. In this paper a multiparameter family of systems of Euler equations is constructed on $M$, and their complete integrability (in the Liouville sense) is proved.
Bibliography: 6 titles.

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English version:
Mathematics of the USSR-Sbornik, 1978, 34:6, 707–713

Bibliographic databases:

UDC: 513.944
MSC: Primary 58F05, 22E60; Secondary 34C35, 34C40

Citation: Dào Trong Thi, “Integrability of the Euler equations on homogeneous symplectic manifolds”, Mat. Sb. (N.S.), 106(148):2(6) (1978), 154–161; Math. USSR-Sb., 34:6 (1978), 707–713

Citation in format AMSBIB
\Bibitem{Dao78} \by D\ao Trong Thi \paper Integrability of the Euler equations on homogeneous symplectic manifolds \jour Mat. Sb. (N.S.) \yr 1978 \vol 106(148) \issue 2(6) \pages 154--161 \mathnet{http://mi.mathnet.ru/msb2562} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=503590} \zmath{https://zbmath.org/?q=an:0394.53024|0422.53018} \transl \jour Math. USSR-Sb. \yr 1978 \vol 34 \issue 6 \pages 707--713 \crossref{https://doi.org/10.1070/SM1978v034n06ABEH001342} `

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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:
1. 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
2. V. V. Trofimov, A. T. Fomenko, “Liouville integrability of Hamiltonian systems on Lie algebras”, Russian Math. Surveys, 39:2 (1984), 1–67
3. A. V. Brailov, “Construction of completely integrable geodesic flows on compact symmetric spaces”, Math. USSR-Izv., 29:1 (1987), 19–31
4. A. V. Bolsinov, “Compatible Poisson brackets on Lie algebras and completeness of families of functions in involution”, Math. USSR-Izv., 38:1 (1992), 69–90
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