Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels

Sergei Agapov, Alexandr Valyuzhenich

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this paper the geodesic flow on the 2-torus in a non-zero magnetic field is considered. Suppose that this flow admits an additional first integral F on N + 2 different energy levels which is polynomial in momenta of an arbitrary degree N with analytic periodic coefficients. It is proved that in this case the magnetic field and the metric are functions of one variable and there exists a linear in momenta first integral on all energy levels.

Original languageEnglish
Pages (from-to)6565-6583
Number of pages19
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume39
Issue number11
DOIs
Publication statusPublished - Nov 2019

Keywords

  • Magnetic geodesic flow, polynomial first integrals
  • QUASI-LINEAR SYSTEM
  • 1ST INTEGRALS
  • HAMILTONIAN-SYSTEMS
  • RIGIDITY
  • Magnetic geodesic flow
  • MECHANICAL SYSTEM
  • polynomial first integrals

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