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 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147429 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| 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| id |
irk-123456789-147429 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1474292019-02-15T01:25:49Z Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem Cariñena, J.F. Rañada, M.F. 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147429 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Cariñena, J.F. Rañada, M.F. |
| spellingShingle |
Cariñena, J.F. Rañada, M.F. Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Cariñena, J.F. Rañada, M.F. |
| author_sort |
Cariñena, J.F. |
| title |
Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem |
| title_short |
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_sort |
quasi-bi-hamiltonian structures of the 2-dimensional kepler problem |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147429 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT carinenajf quasibihamiltonianstructuresofthe2dimensionalkeplerproblem AT ranadamf quasibihamiltonianstructuresofthe2dimensionalkeplerproblem |
| first_indexed |
2023-05-20T17:27:21Z |
| last_indexed |
2023-05-20T17:27:21Z |
| _version_ |
1796153341999316992 |