High-Degree Polynomial Integrals of a Natural System on the Two-Dimensional Torus

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High-Degree Polynomial Integrals of a Natural System on the Two-Dimensional Torus. / Agapov, S. V.

In: Siberian Mathematical Journal, Vol. 64, No. 2, 03.2023, p. 261-268.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{ac21df2442f04be3be77973412802bd5,

title = "High-Degree Polynomial Integrals of a Natural System on the Two-Dimensional Torus",

abstract = "We study a natural mechanical system on the two-dimensional torus which admitsan additional first integral polynomial in momenta of an odd degree $ N $andindependent of the energy integral. For $ N=5,7 $, we obtain the estimateson the number of straight lines in the spectrum of the potential.",

keywords = "517.938, first integral polynomial in momenta, natural mechanical system, spectrum of the potential",

author = "Agapov, {S. V.}",

note = "The author was supported by the Russian Science Foundation (Grant no. 19–11–00044–P). Публикация для корректировки.",

year = "2023",

month = mar,

doi = "10.1134/S0037446623020015",

language = "English",

volume = "64",

pages = "261--268",

journal = "Siberian Mathematical Journal",

issn = "0037-4466",

publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",

number = "2",

}

RIS

TY - JOUR

T1 - High-Degree Polynomial Integrals of a Natural System on the Two-Dimensional Torus

AU - Agapov, S. V.

N1 - The author was supported by the Russian Science Foundation (Grant no. 19–11–00044–P). Публикация для корректировки.

PY - 2023/3

Y1 - 2023/3

N2 - We study a natural mechanical system on the two-dimensional torus which admitsan additional first integral polynomial in momenta of an odd degree $ N $andindependent of the energy integral. For $ N=5,7 $, we obtain the estimateson the number of straight lines in the spectrum of the potential.

AB - We study a natural mechanical system on the two-dimensional torus which admitsan additional first integral polynomial in momenta of an odd degree $ N $andindependent of the energy integral. For $ N=5,7 $, we obtain the estimateson the number of straight lines in the spectrum of the potential.

KW - 517.938

KW - first integral polynomial in momenta

KW - natural mechanical system

KW - spectrum of the potential

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85151085100&origin=inward&txGid=c6d3e433be2a1b651d91c08c53970754

UR - https://www.mendeley.com/catalogue/7debb85b-d033-39a6-934f-4b5befa756ff/

U2 - 10.1134/S0037446623020015

DO - 10.1134/S0037446623020015

M3 - Article

VL - 64

SP - 261

EP - 268

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 2

ER -

ID: 59242956