Research output: Contribution to journal › Article › peer-review
On the Rational Integrals of Two-Dimensional Natural Systems. / Agapov, S. V.; Tursunov, M. M.
In: Siberian Mathematical Journal, Vol. 64, No. 4, 07.2023, p. 787-795.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - On the Rational Integrals of Two-Dimensional Natural Systems
AU - Agapov, S. V.
AU - Tursunov, M. M.
N1 - The first author was supported by the Russian Science Foundation (Grant no. 19–11–00044-P).
PY - 2023/7
Y1 - 2023/7
N2 - We study a natural mechanical system having an additional first integral in the formof a function rational in momenta. One of the authors has proved recently that ifthe configuration space of the system is the two-dimensional torus; then, provided thatthe potential is analytic, the existence of a rational integral withanalytic periodic coefficients and small degrees of the numerator and denominator impliesthe existence of an integral linear in momenta. In the present article, this resultis generalized to the case that the configuration space of the system isthe two-dimensional plane.
AB - We study a natural mechanical system having an additional first integral in the formof a function rational in momenta. One of the authors has proved recently that ifthe configuration space of the system is the two-dimensional torus; then, provided thatthe potential is analytic, the existence of a rational integral withanalytic periodic coefficients and small degrees of the numerator and denominator impliesthe existence of an integral linear in momenta. In the present article, this resultis generalized to the case that the configuration space of the system isthe two-dimensional plane.
KW - 517.938
KW - Hopf equation
KW - first integral rational in momenta
KW - natural system
KW - potential
UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85165587047&origin=inward&txGid=e0172f1564fad384f73cf5788825d671
UR - https://www.mendeley.com/catalogue/562c127b-6ae4-3003-95af-e332a4679f8c/
U2 - 10.1134/S0037446623040018
DO - 10.1134/S0037446623040018
M3 - Article
VL - 64
SP - 787
EP - 795
JO - Siberian Mathematical Journal
JF - Siberian Mathematical Journal
SN - 0037-4466
IS - 4
ER -
ID: 55420049