Convex billiards and a theorem by E. Hops.
Hamiltonian systems, Lagrangian tori and Birkhoffs's theorem.
New semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces
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.
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