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Regular and Chaotic Dynamics, 2015, Volume 20, Issue 6, Pages 667–678
DOI: https://doi.org/10.1134/S1560354715060039 (Mi rcd36) 		 
This article is cited in 10 scientific papers (total in 10 papers)

On an Integrable Magnetic Geodesic Flow on the Two-torus

Iskander A. Taimanovab

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
b Department of Mechanics and Mathematics, Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia
Citations (10)
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DOI: https://doi.org/10.1134/S1560354715060039
Abstract: The magnetic geodesic flow on a flat two-torus with the magnetic field $F=\cos(x)dx\wedge dy$ is completely integrated and the description of all contractible periodic magnetic geodesics is given. It is shown that there are no such geodesics for energy $E\geqslant1/2$, for $E<1/2$ simple periodic magnetic geodesics form two $S^1$-families for which the (fixed energy) action functional is positive and therefore there are no periodic magnetic geodesics for which the action functional is negative.
Keywords: integrable system, magnetic geodesic flow.
Funding agency Grant number
Russian Science Foundation 14-11-00441
The work was supported by RSF (grant 14-11-00441).
Received: 15.08.2015
Accepted: 20.10.2015
Bibliographic databases:
Document Type: Article
MSC: 53D25, 37J35
Language: English
Citation: Iskander A. Taimanov, “On an Integrable Magnetic Geodesic Flow on the Two-torus”, Regul. Chaotic Dyn., 20:6 (2015), 667–678
Citation in format AMSBIB
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\by Iskander A. Taimanov
\paper On an Integrable Magnetic Geodesic Flow on the Two-torus
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 6
\pages 667--678
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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