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

Журнал

Journal of Geometry and Physics
ISSN: 0393-0440

Вых. Данные

Год: 2025, Том: 217, Номер статьи : 105629, Страниц : 16 DOI: 10.1016/j.geomphys.2025.105629

Ключевые слова

Integrable geodesic flow, Polynomial first integral, Semigeodesic coordinates, Semi-Hamiltonian system, Commuting flow, Generalized hodograph method

Авторы

Agapov Sergei ^1,2

Организации

1	Novosibirsk State University
2	Sobolev Institute of Mathematics SB RAS

Информация о финансировании (1)

Российский научный фонд

24-11-00281

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.

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

Поступила в редакцию:	18 янв. 2025 г.
Принята к публикации:	13 авг. 2025 г.
Опубликована online:	20 авг. 2025 г.
Опубликована в печати:	26 авг. 2025 г.

Web of science:	WOS:001565869300001
Scopus:	2-s2.0-105013961685
OpenAlex:	W4413407860

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