Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics
A non-degenerate second-order maximally conformally superintegrable system in dimension 2 naturally gives rise to a quadric with position-dependent coefficients. It is shown how the system's Stäckel class can be obtained from this associated quadric. The Stäckel class of a second-order maximall...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2021 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211173 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics. Andreas Vollmer. SIGMA 17 (2021), 015, 13 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862657019979235328 |
|---|---|
| author | Vollmer, Andreas |
| author_facet | Vollmer, Andreas |
| citation_txt | Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics. Andreas Vollmer. SIGMA 17 (2021), 015, 13 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A non-degenerate second-order maximally conformally superintegrable system in dimension 2 naturally gives rise to a quadric with position-dependent coefficients. It is shown how the system's Stäckel class can be obtained from this associated quadric. The Stäckel class of a second-order maximally conformally superintegrable system is its equivalence class under Stäckel transformations, i.e., under coupling-constant metamorphosis.
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| first_indexed | 2026-03-15T22:13:49Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211173 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T22:13:49Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Vollmer, Andreas 2025-12-25T13:21:43Z 2021 Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics. Andreas Vollmer. SIGMA 17 (2021), 015, 13 pages 1815-0659 2020 Mathematics Subject Classification: 14H70; 70H06; 30F45 arXiv:2010.03638 https://nasplib.isofts.kiev.ua/handle/123456789/211173 https://doi.org/10.3842/SIGMA.2021.015 A non-degenerate second-order maximally conformally superintegrable system in dimension 2 naturally gives rise to a quadric with position-dependent coefficients. It is shown how the system's Stäckel class can be obtained from this associated quadric. The Stäckel class of a second-order maximally conformally superintegrable system is its equivalence class under Stäckel transformations, i.e., under coupling-constant metamorphosis. The author is indebted to Jonathan Kress, Joshua Capel, and Konrad Schobel for many discussions on superintegrability, Stackel transforms, and numerous related topics, and thanks the anonymous referees for contributing valuable suggestions that led to improvements of this paper. A special thank you goes to Konrad Schobel for helpful comments on the manuscript. This paper was principally written when the author was a fellow of the German Research Foundation Deutsche Forschungsgemeinschaft (DFG): Andreas Vollmer acknowledges funding from a DFG research fellowship with the project number 353063958, as well as through a subsequent return fellowship. Andreas Vollmer thanks the University of Stuttgart and the University of New South Wales for their hospitality. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics Article published earlier |
| spellingShingle | Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics Vollmer, Andreas |
| title | Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics |
| title_full | Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics |
| title_fullStr | Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics |
| title_full_unstemmed | Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics |
| title_short | Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics |
| title_sort | stäckel equivalence of non-degenerate superintegrable systems, and invariant quadrics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211173 |
| work_keys_str_mv | AT vollmerandreas stackelequivalenceofnondegeneratesuperintegrablesystemsandinvariantquadrics |