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Mat. Sb., 2000, Volume 191, Number 4, Pages 3–28 (Mi msb468)  

This article is cited in 4 scientific papers (total in 4 papers)

Hamiltonian structures of the first variation equations and symplectic connections

Yu. M. Vorob'ev

Moscow State Institute of Electronics and Mathematics

Abstract: Necessary and sufficient conditions in terms of symplectic connections, ensuring that the first variation equation of a Hamiltonian system along a fixed invariant symplectic submanifold is also a Hamiltonian system with respect to some admissible symplectic structure are obtained. The class of admissible symplectic structures is distinguished by means of the natural condition of compatibility with the symplectic 2-form in the ambient space. Possible obstructions to the existence of a Hamiltonian structure on the first variation equation are investigated.

DOI: https://doi.org/10.4213/sm468

Full text: PDF file (362 kB)
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English version:
Sbornik: Mathematics, 2000, 191:4, 477–502

Bibliographic databases:

UDC: 514.7+517.9
MSC: Primary 58F05, 53C05; Secondary 53C15
Received: 19.03.1999

Citation: Yu. M. Vorob'ev, “Hamiltonian structures of the first variation equations and symplectic connections”, Mat. Sb., 191:4 (2000), 3–28; Sb. Math., 191:4 (2000), 477–502

Citation in format AMSBIB
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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. Espinoza, RF, “Hamiltonian formalism for fiberwise linear dynamical systems”, Boletin de La Sociedad Matematica Mexicana, 6:2 (2000), 213  mathscinet  zmath  isi  elib
    2. A. A. Magazev, I. V. Shirokov, “Hamiltonian systems in variations and the integration of the Jacobi equation on homogeneous spaces”, Russian Math. (Iz. VUZ), 50:8 (2006), 38–49  mathnet  mathscinet  elib
    3. Davila-Rascon, G, “A Hamiltonian approach for skew-product dynamical systems”, Russian Journal of Mathematical Physics, 15:1 (2008), 35  crossref  mathscinet  zmath  adsnasa  isi
    4. Davila-Rascon G., Vorobiev Yu., “Hamiltonian Structures for Projectable Dynamics on Symplectic Fiber Bundles”, Discret. Contin. Dyn. Syst., 33:3, SI (2013), 1077–1088  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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