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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive

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

This article is cited in 1 paper

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.

UDC: 531.01+517.9

Received: January 28, 2020
Revised: January 28, 2020
Accepted: May 18, 2020

DOI: 10.4213/tm4105


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

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