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.
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
\Bibitem{Den20}
\by N.~V.~Denisova
\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
\yr 2020
\vol 310
\pages 143--148
\publ Steklov Math. Inst.
\publaddr Moscow
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2020
\vol 310
\pages 131--136
\crossref{https://doi.org/10.1134/S0081543820050107}
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https://www.mathnet.ru/eng/tm4105
https://doi.org/10.4213/tm4105
https://www.mathnet.ru/eng/tm/v310/p143
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