Invariant Classification and Limits of Maximally Superintegrable Systems in 3D
The invariant classification of superintegrable systems is reviewed and utilized to construct singular limits between the systems. It is shown, by construction, that all superintegrable systems on conformally flat, 3D complex Riemannian manifolds can be obtained from singular limits of a generic sys...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2015 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147015 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Invariant Classification and Limits of Maximally Superintegrable Systems in 3D / J.J. Capel, J.M. Kress, S. Post // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 27 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862697474943090688 |
|---|---|
| author | Capel, J.J. Kress, J.M. Post, S. |
| author_facet | Capel, J.J. Kress, J.M. Post, S. |
| citation_txt | Invariant Classification and Limits of Maximally Superintegrable Systems in 3D / J.J. Capel, J.M. Kress, S. Post // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 27 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The invariant classification of superintegrable systems is reviewed and utilized to construct singular limits between the systems. It is shown, by construction, that all superintegrable systems on conformally flat, 3D complex Riemannian manifolds can be obtained from singular limits of a generic system on the sphere. By using the invariant classification, the limits are geometrically motivated in terms of transformations of roots of the classifying polynomials.
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| first_indexed | 2025-12-07T16:29:55Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147015 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:29:55Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Capel, J.J. Kress, J.M. Post, S. 2019-02-12T20:36:35Z 2019-02-12T20:36:35Z 2015 Invariant Classification and Limits of Maximally Superintegrable Systems in 3D / J.J. Capel, J.M. Kress, S. Post // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 27 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C45; 33D45; 33D80; 81R05; 81R12 DOI:10.3842/SIGMA.2015.038 https://nasplib.isofts.kiev.ua/handle/123456789/147015 The invariant classification of superintegrable systems is reviewed and utilized to construct singular limits between the systems. It is shown, by construction, that all superintegrable systems on conformally flat, 3D complex Riemannian manifolds can be obtained from singular limits of a generic system on the sphere. By using the invariant classification, the limits are geometrically motivated in terms of transformations of roots of the classifying polynomials. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Invariant Classification and Limits of Maximally Superintegrable Systems in 3D Article published earlier |
| spellingShingle | Invariant Classification and Limits of Maximally Superintegrable Systems in 3D Capel, J.J. Kress, J.M. Post, S. |
| title | Invariant Classification and Limits of Maximally Superintegrable Systems in 3D |
| title_full | Invariant Classification and Limits of Maximally Superintegrable Systems in 3D |
| title_fullStr | Invariant Classification and Limits of Maximally Superintegrable Systems in 3D |
| title_full_unstemmed | Invariant Classification and Limits of Maximally Superintegrable Systems in 3D |
| title_short | Invariant Classification and Limits of Maximally Superintegrable Systems in 3D |
| title_sort | invariant classification and limits of maximally superintegrable systems in 3d |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147015 |
| work_keys_str_mv | AT capeljj invariantclassificationandlimitsofmaximallysuperintegrablesystemsin3d AT kressjm invariantclassificationandlimitsofmaximallysuperintegrablesystemsin3d AT posts invariantclassificationandlimitsofmaximallysuperintegrablesystemsin3d |