Geodesic
On the integrable magnetic geodesic flow on a 2-torus
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 868-873

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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. 
@article{SEMR_2015_12_a45,
     author = {S. V. Agapov},
     title = {On the integrable magnetic geodesic flow on a 2-torus},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {868--873},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a45/}
}
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S. V. Agapov. On the integrable magnetic geodesic flow on a 2-torus. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 868-873. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a45/