Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method Full article
| Journal |
Journal of Geometry and Physics
ISSN: 0393-0440 |
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| Output data | Year: 2025, Volume: 217, Article number : 105629, Pages count : 16 DOI: 10.1016/j.geomphys.2025.105629 | ||||
| Tags | Integrable geodesic flow, Polynomial first integral, Semigeodesic coordinates, Semi-Hamiltonian system, Commuting flow, Generalized hodograph method | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Russian Science Foundation | 24-11-00281 |
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.
Cite:
Agapov S.
Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method
Journal of Geometry and Physics. 2025. V.217. 105629 :1-16. DOI: 10.1016/j.geomphys.2025.105629 WOS Scopus OpenAlex
Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method
Journal of Geometry and Physics. 2025. V.217. 105629 :1-16. DOI: 10.1016/j.geomphys.2025.105629 WOS Scopus OpenAlex
Dates:
| Submitted: | Jan 18, 2025 |
| Accepted: | Aug 13, 2025 |
| Published online: | Aug 20, 2025 |
| Published print: | Aug 26, 2025 |
Identifiers:
| Web of science: | WOS:001565869300001 |
| Scopus: | 2-s2.0-105013961685 |
| OpenAlex: | W4413407860 |
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