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TMF, 2008, Volume 156, Number 2, Pages 189–206 (Mi tmf6240)  

This article is cited in 6 scientific papers (total in 6 papers)

Integrable magnetic geodesic flows on Lie groups

A. A. Magazeva, I. V. Shirokova, Yu. A. Yurevichb

a Irtysh Branch of Novosibirsk State Academy of Water Transport
b Omsk State University

Abstract: On Lie group manifolds, we consider right-invariant magnetic geodesic flows associated with 2-cocycles of the corresponding Lie algebras. We investigate the algebra of the integrals of motion of magnetic geodesic flows and also formulate a necessary and sufficient condition for their integrability in quadratures, giving the canonical forms of 2-cocycles for all four-dimensional Lie algebras and selecting integrable cases.

Keywords: Lie group, Lie algebra, cocycle, magnetic geodesic flow, integral of motion, Poisson bracket

DOI: https://doi.org/10.4213/tmf6240

Full text: PDF file (466 kB)
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English version:
Theoretical and Mathematical Physics, 2008, 156:2, 1127–1141

Bibliographic databases:

Received: 19.01.2007
Revised: 02.07.2007

Citation: A. A. Magazev, I. V. Shirokov, Yu. A. Yurevich, “Integrable magnetic geodesic flows on Lie groups”, TMF, 156:2 (2008), 189–206; Theoret. and Math. Phys., 156:2 (2008), 1127–1141

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v156/i2/p189

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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. Dragovic V., Gajic B., Jovanovic B., “Systems of Hess-Appel'rot Type and Zhukovskii Property”, Int J Geom Methods Mod Phys, 6:8 (2009), 1253–1304  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    2. A. A. Magazev, “Integrating Klein–Gordon–Fock equations in an external electromagnetic field on Lie groups”, Theoret. and Math. Phys., 173:3 (2012), 1654–1667  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    3. Magazev A.A., “Simmetrii uravneniya kleina-foka vo vneshnem elektromagnitnom pole”, Omskii nauchnyi vestnik, 2012, no. 110, 29–33  elib
    4. Magazev A.A., “Algebra of Symmetry Operators and Integration of the Klein-Gordon Equation in An External Electromagnetic Field”, Russ. Phys. J., 57:6 (2014), 809–818  crossref  zmath  isi  scopus  scopus
    5. Magazev A.A., “Magnetic Geodesic Flows on Homogeneous Manifolds”, Russ. Phys. J., 57:3 (2014), 312–320  crossref  zmath  isi  scopus  scopus
    6. Inoguchi J.-i., Munteanu M.I., “Magnetic Curves in Tangent Sphere Bundles II”, J. Math. Anal. Appl., 466:2 (2018), 1570–1581  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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