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

2011/12/06 by Michael, Bialy, Andrey Mironov +1
Mathematics · Physics and Astronomy · #35L65 #35L67 #70H06 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:35L65 #msc:35L67 #msc:70H06 #nlin.SI

paper · pdf · doi:10.48550/arxiv.1112.1232

arxiv created 2011/12/06 · arxiv updated 2011/12/07

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.

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