TY - JOUR

T1 - Some Remarks on High Degree Polynomial Integrals of the Magnetic Geodesic Flow on the Two-Dimensional Torus

AU - Agapov, S. V.

AU - Valyuzhenich, A. A.

AU - Shubin, V. V.

N1 - Funding Information: The first author was supported by the Russian Science Foundation (Grant 19–11–00044). Publisher Copyright: © 2021, Pleiades Publishing, Ltd.

PY - 2021/7

Y1 - 2021/7

N2 - 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.

AB - 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.

KW - 517.938

KW - magnetic geodesic flow

KW - polynomial first integral

UR - http://www.scopus.com/inward/record.url?scp=85112650914&partnerID=8YFLogxK

U2 - 10.1134/S0037446621040017

DO - 10.1134/S0037446621040017

M3 - Article

AN - SCOPUS:85112650914

VL - 62

SP - 581

EP - 585

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 4

ER -