High-Degree Polynomial Integrals of a Natural System on the Two-Dimensional Torus

We study a natural mechanical system on the two-dimensional torus which admits an additional first integral polynomial in momenta of an odd degree  and independent of the energy integral. For , we obtain the estimates on the number of straight lines in the spectrum of the potential.

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Bibliographic Details
Published in:Siberian mathematical journal 2023-03, Vol.64 (2), p.261-268
Main Author: Agapov, S. V.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Mechanical systems
Polynomials
Straight lines
Toruses
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Description
Summary:We study a natural mechanical system on the two-dimensional torus which admits an additional first integral polynomial in momenta of an odd degree  and independent of the energy integral. For , we obtain the estimates on the number of straight lines in the spectrum of the potential.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446623020015