Some Remarks on High Degree Polynomial Integrals of the Magnetic Geodesic Flow on the Two-Dimensional Torus

S. V. Agapov, A. A. Valyuzhenich, V. V. Shubin

Research output: Contribution to journalArticlepeer-review

Abstract

We study the magnetic geodesic flow on the two-dimensional torus which admitsan additional high degree first integral polynomial in momenta and is independentof the energy integral. In an earlier work by the first two authors, it wasannounced that if such integral is preserved at a sufficiently many different energy levelsthen there necessarily exists a linear integral at allenergy levels. The proof of the announce was incomplete.Here we finish the proof of the above assertion.

Original languageEnglish
Pages (from-to)581-585
Number of pages5
JournalSiberian Mathematical Journal
Volume62
Issue number4
DOIs
Publication statusPublished - Jul 2021

Keywords

  • 517.938
  • magnetic geodesic flow
  • polynomial first integral

OECD FOS+WOS

  • 1.01 MATHEMATICS

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