Standard

Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method. / Agapov, Sergei.

In: Journal of Geometry and Physics, Vol. 217, 105629, 11.2025.

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

Harvard

Agapov, S 2025, 'Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method', Journal of Geometry and Physics, vol. 217, 105629. https://doi.org/10.1016/j.geomphys.2025.105629

APA

Agapov, S. (2025). Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method. Journal of Geometry and Physics, 217, [105629]. https://doi.org/10.1016/j.geomphys.2025.105629

Vancouver

Agapov S. Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method. Journal of Geometry and Physics. 2025 Nov;217:105629. doi: 10.1016/j.geomphys.2025.105629

Author

Agapov, Sergei. / Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method. In: Journal of Geometry and Physics. 2025 ; Vol. 217.

BibTeX

@article{27e22487cc5c49a789606cc3d6f128d1,
title = "Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method",
abstract = "We study Riemannian metrics on 2-surfaces with integrable geodesic flows such that an additional first integral is high-degree polynomial in momenta. This problem reduces to searching for solutions to certain quasi-linear systems of PDEs which turn out to be semi-Hamiltonian. We construct plenty of local explicit and implicit integrable examples with polynomial first integrals of degrees 3, 4, 5. Our construction is essentially based on applying the generalized hodograph method.",
keywords = "Commuting flow, Generalized hodograph method, Integrable geodesic flow, Polynomial first integral, Semi-Hamiltonian system, Semigeodesic coordinates",
author = "Sergei Agapov",
note = "This work is supported by the grant of the Russian Science Foundation No. 24-11-00281, https://rscf.ru/project/24-11-00281/",
year = "2025",
month = nov,
doi = "10.1016/j.geomphys.2025.105629",
language = "English",
volume = "217",
journal = "Journal of Geometry and Physics",
issn = "0393-0440",
publisher = "Elsevier Science Publishing Company, Inc.",

}

RIS

TY - JOUR

T1 - Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method

AU - Agapov, Sergei

N1 - This work is supported by the grant of the Russian Science Foundation No. 24-11-00281, https://rscf.ru/project/24-11-00281/

PY - 2025/11

Y1 - 2025/11

N2 - We study Riemannian metrics on 2-surfaces with integrable geodesic flows such that an additional first integral is high-degree polynomial in momenta. This problem reduces to searching for solutions to certain quasi-linear systems of PDEs which turn out to be semi-Hamiltonian. We construct plenty of local explicit and implicit integrable examples with polynomial first integrals of degrees 3, 4, 5. Our construction is essentially based on applying the generalized hodograph method.

AB - We study Riemannian metrics on 2-surfaces with integrable geodesic flows such that an additional first integral is high-degree polynomial in momenta. This problem reduces to searching for solutions to certain quasi-linear systems of PDEs which turn out to be semi-Hamiltonian. We construct plenty of local explicit and implicit integrable examples with polynomial first integrals of degrees 3, 4, 5. Our construction is essentially based on applying the generalized hodograph method.

KW - Commuting flow

KW - Generalized hodograph method

KW - Integrable geodesic flow

KW - Polynomial first integral

KW - Semi-Hamiltonian system

KW - Semigeodesic coordinates

UR - https://www.scopus.com/pages/publications/105013961685

UR - https://www.mendeley.com/catalogue/550971b7-8c6f-32c8-bf47-343c9c13a4f7/

U2 - 10.1016/j.geomphys.2025.105629

DO - 10.1016/j.geomphys.2025.105629

M3 - Article

VL - 217

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

M1 - 105629

ER -

ID: 68937537