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Integrable geodesic flows and metrisable second-order ordinary differential equations Научная публикация

Журнал Journal of Geometry and Physics
ISSN: 0393-0440
Вых. Данные Год: 2024, Том: 199, Номер статьи : 105168, Страниц : 14 DOI: 10.1016/j.geomphys.2024.105168
Ключевые слова Metrisable ordinary differential equation, Integrable geodesic flow, Rational first integral, Superintegrability
Авторы Agapov S.V. 1 , Demina Maria V. 2
Организации
1 Sobolev Institute of Mathematics SB RAS, 4 Acad. Koptyug avenue, 630090 Novosibirsk, Russia
2 Department of Applied Mathematics, HSE University, 34 Tallinskaya Street, 123458 Moscow, Russia

Информация о финансировании (2)

1 Институт математики им. С.Л. Соболева СО РАН FWNF-2022-0004
2 Российский научный фонд 19-71-10003

Реферат: It is well known that the system of ordinary differential equations (ODEs) describing geodesic flows of some Riemannian metrics on 2-surfaces admits a projection on a special class of second-order ODEs. In this paper we study in detail this special class of ODEs. We classify all such autonomous ODEs possessing autonomous first integrals that are fractional-quadratic in the first derivative. We construct all the families of integrable geodesic flows related to the ODEs under study. These families are parameterized by two arbitrary functions and contain metrics with superintegrable geodesic flows. We also study the inverse problem and find novel families of second-order ODEs that are related to integrable geodesic flows. We explicitly present first integrals of such ODEs. We find the general structure of metrisable second-order ODEs related to conformal metrics
Библиографическая ссылка: Agapov S.V. , Demina M.V.
Integrable geodesic flows and metrisable second-order ordinary differential equations
Journal of Geometry and Physics. 2024. V.199. 105168 :1-14. DOI: 10.1016/j.geomphys.2024.105168 WOS Scopus РИНЦ OpenAlex
Даты:
Поступила в редакцию: 27 сент. 2023 г.
Принята к публикации: 3 мар. 2024 г.
Опубликована online: 19 мар. 2024 г.
Опубликована в печати: 25 мар. 2024 г.
Идентификаторы БД:
Web of science: WOS:001221887600001
Scopus: 2-s2.0-85188062401
РИНЦ: 67128878
OpenAlex: W4392603592
Цитирование в БД:
БД Цитирований
Scopus 1
Альметрики: