Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials
The structure theory for the quadratic algebra generated by first and second order constants of the motion for 2D second order superintegrable systems with nondegenerate (3-parameter) and or 2-parameter potentials is well understood, but the results for the strictly 1-parameter case have been incomp...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2009 |
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149255 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials / E.G. Kalnins, J.M. Kress, Willard Miller Jr., S. Post // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 27 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862534675282526208 |
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| author | Kalnins, E.G. Kress, J.M. Post, S. Miller Jr., W. |
| author_facet | Kalnins, E.G. Kress, J.M. Post, S. Miller Jr., W. |
| citation_txt | Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials / E.G. Kalnins, J.M. Kress, Willard Miller Jr., S. Post // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 27 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The structure theory for the quadratic algebra generated by first and second order constants of the motion for 2D second order superintegrable systems with nondegenerate (3-parameter) and or 2-parameter potentials is well understood, but the results for the strictly 1-parameter case have been incomplete. Here we work out this structure theory and prove that the quadratic algebra generated by first and second order constants of the motion for systems with 4 second order constants of the motion must close at order three with the functional relationship between the 4 generators of order four. We also show that every 1-parameter superintegrable system is Stäckel equivalent to a system on a constant curvature space.
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| first_indexed | 2025-11-24T09:17:44Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149255 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T09:17:44Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kalnins, E.G. Kress, J.M. Post, S. Miller Jr., W. 2019-02-19T19:26:21Z 2019-02-19T19:26:21Z 2009 Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials / E.G. Kalnins, J.M. Kress, Willard Miller Jr., S. Post // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 27 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 20C99; 20C35; 22E70 https://nasplib.isofts.kiev.ua/handle/123456789/149255 The structure theory for the quadratic algebra generated by first and second order constants of the motion for 2D second order superintegrable systems with nondegenerate (3-parameter) and or 2-parameter potentials is well understood, but the results for the strictly 1-parameter case have been incomplete. Here we work out this structure theory and prove that the quadratic algebra generated by first and second order constants of the motion for systems with 4 second order constants of the motion must close at order three with the functional relationship between the 4 generators of order four. We also show that every 1-parameter superintegrable system is Stäckel equivalent to a system on a constant curvature space. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials Article published earlier |
| spellingShingle | Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials Kalnins, E.G. Kress, J.M. Post, S. Miller Jr., W. |
| title | Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials |
| title_full | Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials |
| title_fullStr | Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials |
| title_full_unstemmed | Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials |
| title_short | Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials |
| title_sort | structure theory for second order 2d superintegrable systems with 1-parameter potentials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149255 |
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