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...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2016 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2016
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| Онлайн доступ: | https://nasplib.isofts.kiev.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| _version_ | 1862712225951645696 |
|---|---|
| author | Cariñena, J.F. Rañada, M.F. |
| author_facet | Cariñena, J.F. Rañada, M.F. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2025-12-07T17:35:29Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147429 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:35:29Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Cariñena, J.F. Rañada, M.F. 2019-02-14T18:31:06Z 2019-02-14T18:31:06Z 2016 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. 1815-0659 2010 Mathematics Subject Classification: 37J15; 37J35; 70H06; 70H33 DOI:10.3842/SIGMA.2016.010 https://nasplib.isofts.kiev.ua/handle/123456789/147429 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. This paper is a contribution to the Special Issue on Analytical Mechanics and Dif ferential Geometry in honour
 of Sergio Benenti. The full collection is available at http://www.emis.de/journals/SIGMA/Benenti.html.
 This work has been supported by the research projects MTM–2012–33575 (MICINN, Madrid)
 and DGA-E24/1 (DGA, Zaragoza). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem Article published earlier |
| spellingShingle | Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem Cariñena, J.F. Rañada, M.F. |
| title | Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem |
| title_full | Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem |
| title_fullStr | Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem |
| title_full_unstemmed | Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem |
| title_short | Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem |
| title_sort | quasi-bi-hamiltonian structures of the 2-dimensional kepler problem |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147429 |
| work_keys_str_mv | AT carinenajf quasibihamiltonianstructuresofthe2dimensionalkeplerproblem AT ranadamf quasibihamiltonianstructuresofthe2dimensionalkeplerproblem |