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This article is cited in 2 scientific papers (total in 2 papers)
High-degree polynomial integrals of a natural system on the two-dimensional torus
S. V. Agapovab a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Abstract:
We study a natural mechanical system on the two-dimensional torus which admits an additional first integral polynomial in momenta of an odd degree $N$ and independent of the energy integral. For $N=5, 7$, we obtain the estimates on the number of straight lines in the spectrum of the potential.
Keywords:
natural mechanical system, first integral polynomial in momenta, spectrum of the potential.
Received: 13.07.2022 Revised: 25.07.2022 Accepted: 15.08.2022
Citation:
S. V. Agapov, “High-degree polynomial integrals of a natural system on the two-dimensional torus”, Sibirsk. Mat. Zh., 64:2 (2023), 243–251; Siberian Math. J., 64:2 (2023), 261–268
Linking options:
https://www.mathnet.ru/eng/smj7758 https://www.mathnet.ru/eng/smj/v64/i2/p243
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