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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, Number 3, Pages 3–9 (Mi ivm7240)  
This article is cited in 2 scientific papers (total in 2 papers)

Phase flows and vector Hamiltonians

V. N. Dumachev

Chair of Mathematics, Voronezh Institute of the Ministry of Internal Affairs of the Russia, Voronezh, Russia
Full-text PDF (165 kB) Citations (2)
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Abstract: We present generalization of the Nambu mechanics on the base of Liouville theorem. We prove that Poisson structure of n-dimensional multi-symplectic phase space is induced by (n−1) Hamilton k-vectors fields. Each of these fields requires introduction of k-hamiltonians.
Keywords: Liouville theorem, Hamilton vectors fields.
Received: 30.06.2009
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, Volume 55, Issue 3, Pages 1–7
DOI: https://doi.org/10.3103/S1066369X11030017
Bibliographic databases:
Document Type: Article
UDC: 514.8
Language: Russian
Citation: V. N. Dumachev, “Phase flows and vector Hamiltonians”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 3, 3–9; Russian Math. (Iz. VUZ), 55:3 (2011), 1–7
Citation in format AMSBIB
\Bibitem{Dum11}
\by V.~N.~Dumachev
\paper Phase flows and vector Hamiltonians
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 3
\pages 3--9
\mathnet{http://mi.mathnet.ru/ivm7240}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2919802}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 3
\pages 1--7
\crossref{https://doi.org/10.3103/S1066369X11030017}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952998964}
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  • https://www.mathnet.ru/eng/ivm7240
  • https://www.mathnet.ru/eng/ivm/y2011/i3/p3
    • This publication is cited in the following 2 articles:
    1. Esen O. Guha P., “on the Quest For Generalized Hamiltonian Descriptions of 3D-Flows Generated By the Curl of a Vector Potential”, Int. J. Geom. Methods Mod. Phys., 17:3 (2020), 2050042  crossref  mathscinet  isi  scopus
    2. V. N. Dumachev, “Vector hamiltonians in Nambu mechanics”, Russian Math. (Iz. VUZ), 62:2 (2018), 28–33  mathnet  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    Abstract page:286
    Full-text PDF :79
    References:50
    First page:10
     
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