Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem
The existence of quasi-bi-Hamiltonian structures for the Kepler problem is studied. We first relate the superintegrability of the system with the existence of two complex functions endowed with very interesting Poisson bracket properties and then we prove the existence of a quasi-bi-Hamiltonian stru...
Збережено в:
| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147429 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem / J.F. Cariñena, M.F. Rañada // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 36 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | The existence of quasi-bi-Hamiltonian structures for the Kepler problem is studied. We first relate the superintegrability of the system with the existence of two complex functions endowed with very interesting Poisson bracket properties and then we prove the existence of a quasi-bi-Hamiltonian structure by making use of these two functions. The paper can be considered as divided in two parts. In the first part a quasi-bi-Hamiltonian structure is obtained by making use of polar coordinates and in the second part a new quasi-bi-Hamiltonian structure is obtained by making use of the separability of the system in parabolic coordinates. |
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