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

Misha Bialy, Andrey Mironov

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)1596-1604
Number of pages9
JournalCentral European Journal of Mathematics
Volume10
Issue number5
DOIs
StatePublished - Oct 2012

Keywords

  • Integral of motion
  • Magnetic geodesic flows
  • Riemann invariants
  • Systems of hydrodynamic type

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