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 |
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Страницы (с-по) | 6565-6583 |
Число страниц | 19 |
Журнал | Discrete and Continuous Dynamical Systems- Series A |
Том | 39 |
Номер выпуска | 11 |
DOI | |
Состояние | Опубликовано - ноя 2019 |
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