Trudy Mat. Inst. Steklova, 2020, Volume 310, Pages 143–148
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
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.
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Proceedings of the Steklov Institute of Mathematics, 2020, 310, 131–136
Received: January 28, 2020
Revised: January 28, 2020
Accepted: May 18, 2020
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
\paper On Momentum-Polynomial Integrals of a Reversible Hamiltonian System of a Certain Form
\inbook Selected issues of mathematics and mechanics
\bookinfo Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov
\serial Trudy Mat. Inst. Steklova
\publ Steklov Math. Inst.
\jour Proc. Steklov Inst. Math.
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