We consider magnetic geodesic flows on the two-torus. We prove that the question of existence of polynomial in momenta first integrals on one energy level leads to a semi-Hamiltonian system of quasi-linear equations, i.e. in the hyperbolic regions the system has Riemann invariants and can be written in conservation laws form.
@article{bwmeta1.element.doi-10_2478_s11533-012-0045-3,
author = {Misha Bialy and Andrey Mironov},
title = {New semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {1596-1604},
zbl = {1259.35137},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0045-3}
}
Misha Bialy; Andrey Mironov. New semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces. Open Mathematics, Tome 10 (2012) pp. 1596-1604. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0045-3/
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