On rational integrals of geodesic flows on 2-surfaces Full article
| Journal |
Regular and Chaotic Dynamics
ISSN: 1560-3547 , E-ISSN: 1468-4845 |
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| Output data | Year: 2025, Volume: 31, Number: 1, Pages: 150-160 Pages count : 11 DOI: 10.1134/S1560354725540019 | ||
| Tags | integrable geodesic flow, rational first integral, semi-geodesic coordinates, classical hodograph method, Euler-Poisson-Darboux equation | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0004 |
Abstract:
In this paper we study Riemannian metrics on 2-surfaces with integrable geodesic ows by means of an additional rational in momenta rst integral. This problem is reduced to a quasi-linear system of PDEs. We construct solutions to this system via the classical hodograph method. These solutions give rise to local examples of metrics and rational integrals. Some of the constructed metrics have a very simple form. A family of implicit integrable examples parameterized by two arbitrary functions of one variable is also provided.
Cite:
Agapov S.V.
On rational integrals of geodesic flows on 2-surfaces
Regular and Chaotic Dynamics. 2025. V.31. N1. P.150-160. DOI: 10.1134/S1560354725540019 WOS Scopus РИНЦ
On rational integrals of geodesic flows on 2-surfaces
Regular and Chaotic Dynamics. 2025. V.31. N1. P.150-160. DOI: 10.1134/S1560354725540019 WOS Scopus РИНЦ
Dates:
| Submitted: | Aug 4, 2025 |
| Accepted: | Oct 16, 2025 |
| Published online: | Dec 20, 2025 |
| Published print: | Mar 16, 2026 |
Identifiers:
| ≡ Web of science: | WOS:001642720400001 |
| ≡ Scopus: | 2-s2.0-105025424973 |
| ≡ Elibrary: | 89062871 |