# New semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces

Open Mathematics (2012)

- Volume: 10, Issue: 5, page 1596-1604
- ISSN: 2391-5455

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topMisha Bialy, and Andrey Mironov. "New semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces." Open Mathematics 10.5 (2012): 1596-1604. <http://eudml.org/doc/269054>.

@article{MishaBialy2012,

abstract = {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.},

author = {Misha Bialy, Andrey Mironov},

journal = {Open Mathematics},

keywords = {Integral of motion; Magnetic geodesic flows; Riemann invariants; Systems of hydrodynamic type; integral of motion; magnetic geodesic flows; systems of hydrodynamic type; polynomial in momenta first integrals},

language = {eng},

number = {5},

pages = {1596-1604},

title = {New semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces},

url = {http://eudml.org/doc/269054},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Misha Bialy

AU - Andrey Mironov

TI - New semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces

JO - Open Mathematics

PY - 2012

VL - 10

IS - 5

SP - 1596

EP - 1604

AB - 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.

LA - eng

KW - Integral of motion; Magnetic geodesic flows; Riemann invariants; Systems of hydrodynamic type; integral of motion; magnetic geodesic flows; systems of hydrodynamic type; polynomial in momenta first integrals

UR - http://eudml.org/doc/269054

ER -

## References

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