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

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

Journal

Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260

Output data

Year: 2021, Volume: 62, Number: 4, Pages: 581-585 Pages count : 5 DOI: 10.1134/S0037446621040017

Funding (1)

Russian Science Foundation

19-11-00044

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. © 2021, Pleiades Publishing, Ltd.

Agapov S.V. , Valyuzhenich A.A. , Shubin V.V.
Some Remarks on High Degree Polynomial Integrals of the Magnetic Geodesic Flow on the Two-Dimensional Torus
Siberian Mathematical Journal. 2021. V.62. N4. P.581-585. DOI: 10.1134/S0037446621040017 WOS Scopus OpenAlex

Agapov S.V. , Valyuzhenich A.A. , Shubin V.V.
Некоторые замечания о полиномиальных интегралах высокой степени магнитного геодезического потока на двумерном торе
Сибирский математический журнал. 2021. V.62. N4. P.715-720. DOI: 10.33048/smzh.2021.62.401 OpenAlex

Web of science:	WOS:000682525600001
Scopus:	2-s2.0-85112650914
OpenAlex:	W3198188101

DB	Citing
Scopus	2
Web of science	1
OpenAlex	2