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Trudy Mat. Inst. Steklova, 2020, Volume 310, Pages 143–148 (Mi tm4105)  

On Momentum-Polynomial Integrals of a Reversible Hamiltonian System of a Certain Form

N. V. Denisova

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119991 Russia

Abstract: The problem of first integrals that are polynomial in momenta is considered for the equations of motion of a particle on a two-dimensional Euclidean torus in a force field with even potential. Of special interest is the case when the spectrum of the potential lies on four straight lines such that the angle between any two of them is a multiple of $\pi /4$. With the help of perturbation theory, it is proved that there are no additional polynomial integrals of any degree that are independent of the Hamiltonian function.

DOI: https://doi.org/10.4213/tm4105

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English version:
Proceedings of the Steklov Institute of Mathematics, 2020, 310, 131–136

Bibliographic databases:

UDC: 531.01+517.9
Received: January 28, 2020
Revised: January 28, 2020
Accepted: May 18, 2020

Citation: N. V. Denisova, “On Momentum-Polynomial Integrals of a Reversible Hamiltonian System of a Certain Form”, Selected issues of mathematics and mechanics, Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov, Trudy Mat. Inst. Steklova, 310, Steklov Math. Inst., Moscow, 2020, 143–148; Proc. Steklov Inst. Math., 310 (2020), 131–136

Citation in format AMSBIB
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\paper On Momentum-Polynomial Integrals of a Reversible Hamiltonian System of a Certain Form
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\vol 310
\pages 143--148
\publ Steklov Math. Inst.
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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