Equivalent Integrable Metrics on the Sphere with Quartic Invariants
We discuss canonical transformations relating well-known geodesic flows on the cotangent bundle of the sphere to a set of geodesic flows with quartic invariants. By adding various potentials to the corresponding geodesic Hamiltonians, we can construct new integrable systems on the sphere with quarti...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2022 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2022
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211810 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Equivalent Integrable Metrics on the Sphere with Quartic Invariants. Andrey V. Tsiganov. SIGMA 18 (2022), 094, 19 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862568435831013376 |
|---|---|
| author | Tsiganov, Andrey V. |
| author_facet | Tsiganov, Andrey V. |
| citation_txt | Equivalent Integrable Metrics on the Sphere with Quartic Invariants. Andrey V. Tsiganov. SIGMA 18 (2022), 094, 19 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We discuss canonical transformations relating well-known geodesic flows on the cotangent bundle of the sphere to a set of geodesic flows with quartic invariants. By adding various potentials to the corresponding geodesic Hamiltonians, we can construct new integrable systems on the sphere with quartic invariants.
|
| first_indexed | 2026-03-13T11:13:36Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211810 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T11:13:36Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Tsiganov, Andrey V. 2026-01-12T10:14:54Z 2022 Equivalent Integrable Metrics on the Sphere with Quartic Invariants. Andrey V. Tsiganov. SIGMA 18 (2022), 094, 19 pages 1815-0659 2020 Mathematics Subject Classification: 37J35; 70H06; 70H45 arXiv:2201.09576 https://nasplib.isofts.kiev.ua/handle/123456789/211810 https://doi.org/10.3842/SIGMA.2022.094 We discuss canonical transformations relating well-known geodesic flows on the cotangent bundle of the sphere to a set of geodesic flows with quartic invariants. By adding various potentials to the corresponding geodesic Hamiltonians, we can construct new integrable systems on the sphere with quartic invariants. We are very grateful to the referees for their thorough analysis of the manuscript, constructive suggestions, and proposed corrections, which certainly led to a more profound discussion of the results. The work was supported by the Russian Science Foundation (project 21-11-00141). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Equivalent Integrable Metrics on the Sphere with Quartic Invariants Article published earlier |
| spellingShingle | Equivalent Integrable Metrics on the Sphere with Quartic Invariants Tsiganov, Andrey V. |
| title | Equivalent Integrable Metrics on the Sphere with Quartic Invariants |
| title_full | Equivalent Integrable Metrics on the Sphere with Quartic Invariants |
| title_fullStr | Equivalent Integrable Metrics on the Sphere with Quartic Invariants |
| title_full_unstemmed | Equivalent Integrable Metrics on the Sphere with Quartic Invariants |
| title_short | Equivalent Integrable Metrics on the Sphere with Quartic Invariants |
| title_sort | equivalent integrable metrics on the sphere with quartic invariants |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211810 |
| work_keys_str_mv | AT tsiganovandreyv equivalentintegrablemetricsonthespherewithquarticinvariants |