New Semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces
Mathematical Physics
2011-12-07 v1 math.MP
Exactly Solvable and Integrable Systems
Abstract
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.
Keywords
Cite
@article{arxiv.1112.1232,
title = {New Semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces},
author = {Michael and Bialy and Andrey Mironov},
journal= {arXiv preprint arXiv:1112.1232},
year = {2011}
}