On rational integrals of geodesic flows on 2-surfaces Научная публикация
| Журнал |
Regular and Chaotic Dynamics
ISSN: 1560-3547 , E-ISSN: 1468-4845 |
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| Вых. Данные | Год: 2025, Том: 31, Номер: 1, Страницы: 1-11 Страниц : 11 DOI: 10.1134/S1560354725540019 | ||
| Ключевые слова | integrable geodesic flow, rational first integral, semi-geodesic coordinates, classical hodograph method, Euler-Poisson-Darboux equation | ||
| Авторы |
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| Организации |
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Информация о финансировании (1)
| 1 | Институт математики им. С.Л. Соболева СО РАН | FWNF-2022-0004 |
Реферат:
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.
Библиографическая ссылка:
Agapov S.V.
On rational integrals of geodesic flows on 2-surfaces
Regular and Chaotic Dynamics. 2025. V.31. N1. P.1-11. DOI: 10.1134/S1560354725540019 WOS
On rational integrals of geodesic flows on 2-surfaces
Regular and Chaotic Dynamics. 2025. V.31. N1. P.1-11. DOI: 10.1134/S1560354725540019 WOS
Даты:
| Поступила в редакцию: | 4 авг. 2025 г. |
| Принята к публикации: | 16 окт. 2025 г. |
| Опубликована online: | 20 дек. 2025 г. |
Идентификаторы БД:
| Web of science: | WOS:001642720400001 |
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