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Sib. Èlektron. Mat. Izv., 2015, Volume 12, Pages 868–873 (Mi semr636)  

This article is cited in 2 scientific papers (total in 2 papers)

Geometry and topology

On the integrable magnetic geodesic flow on a 2-torus

S. V. Agapov

Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: In this paper the magnetic geodesic flow on a 2-torus is considered. We study a semi-hamiltonian quasi-linear PDEs which is equivalent to the existence of polynomial in momenta first integral of magnetic geodesic flow on fixed energy level. It is known that diagonal metric associated with this system is Egorov one if degree of the first integral is equal to 2 or 3. In this paper we prove this fact in the case of existence of the first integral of any degree.

Keywords: semi-hamiltonian systems, Egorov metrics.

Funding Agency Grant Number
Russian Science Foundation 14-11-00441


DOI: https://doi.org/10.17377/semi.2015.12.073

Full text: PDF file (132 kB)
References: PDF file   HTML file

UDC: 517.938
MSC: 35L65, 37J35, 70H06
Received October 21, 2015, published November 30, 2015

Citation: S. V. Agapov, “On the integrable magnetic geodesic flow on a 2-torus”, Sib. Èlektron. Mat. Izv., 12 (2015), 868–873

Citation in format AMSBIB
\Bibitem{Aga15}
\by S.~V.~Agapov
\paper On the integrable magnetic geodesic flow on a 2-torus
\jour Sib. \`Elektron. Mat. Izv.
\yr 2015
\vol 12
\pages 868--873
\mathnet{http://mi.mathnet.ru/semr636}
\crossref{https://doi.org/10.17377/semi.2015.12.073}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. A. Taimanov, “On first integrals of geodesic flows on a two-torus”, Proc. Steklov Inst. Math., 295 (2016), 225–242  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. S. V. Agapov, M. Bialy, A. E. Mironov, “Integrable magnetic geodesic flows on 2-torus: new examples via quasi-linear system of pdes”, Commun. Math. Phys., 351:3 (2017), 993–1007  crossref  mathscinet  zmath  isi  scopus
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