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

doi:10.1134/S0037446621040017

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

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

Аннотация

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.

Язык оригинала	английский
Страницы (с-по)	581-585
Число страниц	5
Журнал	Siberian Mathematical Journal
Том	62
Номер выпуска	4
DOI	https://doi.org/10.1134/S0037446621040017
Состояние	Опубликовано - июл 2021

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1.01 МАТЕМАТИКА

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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.",

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Some Remarks on High Degree Polynomial Integrals of the Magnetic Geodesic Flow on the Two-Dimensional Torus. / Agapov, S. V.; Valyuzhenich, A. A.; Shubin, V. V.

В: Siberian Mathematical Journal, Том 62, № 4, 07.2021, стр. 581-585.

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

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