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

Sergei Agapov; Alexandr Valyuzhenich

doi:10.3934/dcds.2019285

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

Sergei Agapov, Alexandr Valyuzhenich

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

2 Цитирования (Scopus)

Аннотация

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.

Язык оригинала	английский
Страницы (с-по)	6565-6583
Число страниц	19
Журнал	Discrete and Continuous Dynamical Systems- Series A
Том	39
Номер выпуска	11
DOI	https://doi.org/10.3934/dcds.2019285
Состояние	Опубликовано - ноя 2019

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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.",

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

author = "Sergei Agapov and Alexandr Valyuzhenich",

year = "2019",

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Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels. / Agapov, Sergei; Valyuzhenich, Alexandr.

В: Discrete and Continuous Dynamical Systems- Series A, Том 39, № 11, 11.2019, стр. 6565-6583.

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

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