New Semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces

Details New Semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces New Semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces

2011-12-06

arxiv.org/abs/1112.1232v1

Physics

Mathematical Physics

Scientific paper

We consider magnetic geodesic flows on the 2-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.

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