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 Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 6, Pages 1345–1352 (Mi izv1344)

On the Hamiltonian property of an arbitrary evolution system on the set of stationary points of its integral

O. I. Mokhov

Abstract: The Bogoyavlenskii–Novikov principle concerning the connection between stationary and nonstationary problems is generalized. It is proved that an arbitrary evolution system is Hamiltonian on the set of stationary points of its local integral.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1988, 31:3, 657–664

Bibliographic databases:

UDC: 517.91
MSC: Primary 58F05; Secondary 70H05

Citation: O. I. Mokhov, “On the Hamiltonian property of an arbitrary evolution system on the set of stationary points of its integral”, Izv. Akad. Nauk SSSR Ser. Mat., 51:6 (1987), 1345–1352; Math. USSR-Izv., 31:3 (1988), 657–664

Citation in format AMSBIB
\Bibitem{Mok87} \by O.~I.~Mokhov \paper On the Hamiltonian property of an arbitrary evolution system on the set of stationary points of its integral \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1987 \vol 51 \issue 6 \pages 1345--1352 \mathnet{http://mi.mathnet.ru/izv1344} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=933968} \zmath{https://zbmath.org/?q=an:0694.58014|0671.58009} \transl \jour Math. USSR-Izv. \yr 1988 \vol 31 \issue 3 \pages 657--664 \crossref{https://doi.org/10.1070/IM1988v031n03ABEH001095} 

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This publication is cited in the following articles:
1. Funct. Anal. Appl., 24:3 (1990), 247–249
2. A. P. Fordy, A. B. Shabat, A. P. Veselov, “Factorization and Poisson correspondences”, Theoret. and Math. Phys., 105:2 (1995), 1369–1386
3. Allan P. Fordy, “Stationary flows: Hamiltonian structures and canonical transformations”, Physica D: Nonlinear Phenomena, 87:1-4 (1995), 20
4. E. V. Ferapontov, R. A. Sharipov, “On first-order conservation laws for systems of hydronamic type equations”, Theoret. and Math. Phys., 108:1 (1996), 937–952
5. E.V. Ferapontov, A.P. Fordy, “Non-homogeneous systems of hydrodynamic type, related to quadratic Hamiltonians with electromagnetic term”, Physica D: Nonlinear Phenomena, 108:4 (1997), 350
6. O. I. Mokhov, “Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems”, Russian Math. Surveys, 53:3 (1998), 515–622
7. Monica Ugaglia, “On the Hamiltonian and Lagrangian structures of time-dependent reductions of evolutionary PDEs”, Differential Geometry and its Applications, 16:1 (2002), 1
8. O. I. Mokhov, N. A. Strizhova, “Integriruemost po Liuvillyu reduktsii uravnenii assotsiativnosti na mnozhestvo statsionarnykh tochek integrala v sluchae trekh primarnykh polei”, UMN, 74:2(446) (2019), 191–192
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