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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 156, Number 2, Pages 189–206
DOI: https://doi.org/10.4213/tmf6240 (Mi tmf6240) 		 
This article is cited in 17 scientific papers (total in 17 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
Full-text PDF (466 kB) Citations (17)
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DOI: https://doi.org/10.4213/tmf6240
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.
Received: 19.01.2007
Revised: 02.07.2007
English version:
Theoretical and Mathematical Physics, 2008, Volume 156, Issue 2, Pages 1127–1141
DOI: https://doi.org/10.1007/s11232-008-0083-y
Bibliographic databases:
Language: Russian
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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    • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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