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On rotation invariant integrable systems. / Tsiganov, A.V.

In: Izvestiya Mathematics, Vol. 88, No. 2, 2024, p. 389–409.

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

Harvard

Tsiganov, AV 2024, 'On rotation invariant integrable systems', Izvestiya Mathematics, vol. 88, no. 2, pp. 389–409. https://doi.org/10.4213/im9506e

APA

Tsiganov, A. V. (2024). On rotation invariant integrable systems. Izvestiya Mathematics, 88(2), 389–409. https://doi.org/10.4213/im9506e

Vancouver

Tsiganov AV. On rotation invariant integrable systems. Izvestiya Mathematics. 2024;88(2):389–409. https://doi.org/10.4213/im9506e

Author

Tsiganov, A.V. / On rotation invariant integrable systems. In: Izvestiya Mathematics. 2024 ; Vol. 88, No. 2. pp. 389–409.

BibTeX

@article{e068bf3473cc4be3a7772529a23bb7f0,
title = "On rotation invariant integrable systems",
abstract = "The problem of finding the first integrals of the Newton equations in the $n$-dimensional Euclidean space is reduced to that of finding two integrals of motion on the Lie algebra $\mathrm{so}(4)$ which are invariant under $m\geq n-2$ rotation symmetry fields. As an example, we obtain several families of integrable and superintegrable systems with first, second, and fourth-degree integrals of motion in the momenta. The corresponding Hamilton-Jacobi equation does not admit separation variables in any of the known curvilinear orthogonal coordinate systems in the Euclidean space.",
author = "A.V. Tsiganov",
year = "2024",
doi = "10.4213/im9506e",
language = "English",
volume = "88",
pages = "389–409",
journal = "Izvestiya Mathematics",
issn = "1064-5632",
publisher = "IOP Publishing Ltd.",
number = "2",

}

RIS

TY - JOUR

T1 - On rotation invariant integrable systems

AU - Tsiganov, A.V.

PY - 2024

Y1 - 2024

N2 - The problem of finding the first integrals of the Newton equations in the $n$-dimensional Euclidean space is reduced to that of finding two integrals of motion on the Lie algebra $\mathrm{so}(4)$ which are invariant under $m\geq n-2$ rotation symmetry fields. As an example, we obtain several families of integrable and superintegrable systems with first, second, and fourth-degree integrals of motion in the momenta. The corresponding Hamilton-Jacobi equation does not admit separation variables in any of the known curvilinear orthogonal coordinate systems in the Euclidean space.

AB - The problem of finding the first integrals of the Newton equations in the $n$-dimensional Euclidean space is reduced to that of finding two integrals of motion on the Lie algebra $\mathrm{so}(4)$ which are invariant under $m\geq n-2$ rotation symmetry fields. As an example, we obtain several families of integrable and superintegrable systems with first, second, and fourth-degree integrals of motion in the momenta. The corresponding Hamilton-Jacobi equation does not admit separation variables in any of the known curvilinear orthogonal coordinate systems in the Euclidean space.

UR - https://www.mendeley.com/catalogue/3a00dce5-7e1d-30cc-ac1c-ab45b50faabb/

U2 - 10.4213/im9506e

DO - 10.4213/im9506e

M3 - Article

VL - 88

SP - 389

EP - 409

JO - Izvestiya Mathematics

JF - Izvestiya Mathematics

SN - 1064-5632

IS - 2

ER -

ID: 118313453