Doubly Exotic th-Order Superintegrable Classical Systems Separating in Cartesian Coordinates
Superintegrable classical Hamiltonian systems in two-dimensional Euclidean space ₂ are explored. The study is restricted to Hamiltonians allowing separation of variables (, ) = ₁() + ₂() in Cartesian coordinates. In particular, the Hamiltonian ℋ admits a polynomial integral of order > 2. Only do...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2022 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2022
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211629 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Doubly Exotic th-Order Superintegrable Classical Systems Separating in Cartesian Coordinates. İsmet Yurduşen, Adrián Mauricio Escobar-Ruiz and Irlanda Palma y Meza Montoya. SIGMA 18 (2022), 039, 20 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862624452716527616 |
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| author | Yurduşen, İsmet Escobar-Ruiz, Adrián Mauricio Palma y Meza Montoya, Irlanda |
| author_facet | Yurduşen, İsmet Escobar-Ruiz, Adrián Mauricio Palma y Meza Montoya, Irlanda |
| citation_txt | Doubly Exotic th-Order Superintegrable Classical Systems Separating in Cartesian Coordinates. İsmet Yurduşen, Adrián Mauricio Escobar-Ruiz and Irlanda Palma y Meza Montoya. SIGMA 18 (2022), 039, 20 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Superintegrable classical Hamiltonian systems in two-dimensional Euclidean space ₂ are explored. The study is restricted to Hamiltonians allowing separation of variables (, ) = ₁() + ₂() in Cartesian coordinates. In particular, the Hamiltonian ℋ admits a polynomial integral of order > 2. Only doubly exotic potentials are considered. These are potentials where none of their separated parts obey any linear ordinary differential equation. An improved procedure to calculate these higher-order superintegrable systems is described in detail. The two basic building blocks of the formalism are non-linear compatibility conditions and the algebra of the integrals of motion. The case = 5, where doubly exotic confining potentials appear for the first time, is completely solved to illustrate the present approach. The general case > 2 and a formulation of the inverse problem in superintegrability are briefly discussed as well.
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| first_indexed | 2026-03-14T14:52:47Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211629 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T14:52:47Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Yurduşen, İsmet Escobar-Ruiz, Adrián Mauricio Palma y Meza Montoya, Irlanda 2026-01-07T13:41:10Z 2022 Doubly Exotic th-Order Superintegrable Classical Systems Separating in Cartesian Coordinates. İsmet Yurduşen, Adrián Mauricio Escobar-Ruiz and Irlanda Palma y Meza Montoya. SIGMA 18 (2022), 039, 20 pages 1815-0659 2020 Mathematics Subject Classification: 70H06; 70H33; 70H50 arXiv:2112.01735 https://nasplib.isofts.kiev.ua/handle/123456789/211629 https://doi.org/10.3842/SIGMA.2022.039 Superintegrable classical Hamiltonian systems in two-dimensional Euclidean space ₂ are explored. The study is restricted to Hamiltonians allowing separation of variables (, ) = ₁() + ₂() in Cartesian coordinates. In particular, the Hamiltonian ℋ admits a polynomial integral of order > 2. Only doubly exotic potentials are considered. These are potentials where none of their separated parts obey any linear ordinary differential equation. An improved procedure to calculate these higher-order superintegrable systems is described in detail. The two basic building blocks of the formalism are non-linear compatibility conditions and the algebra of the integrals of motion. The case = 5, where doubly exotic confining potentials appear for the first time, is completely solved to illustrate the present approach. The general case > 2 and a formulation of the inverse problem in superintegrability are briefly discussed as well. İY and AMER, during a sabbatical leave and a postdoctoral academic stay at the Centre de Recherches Mathématiques, Université de Montréal, respectively, were introduced to the subject of higher-order superintegrability by Pavel Winternitz. His enormous influence is present in this study as it is in the whole subject. It is with admiration and great affection that we dedicate this paper to his memory. We thank the anonymous referees and the editor for their valuable comments and constructive suggestions on the manuscript. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Doubly Exotic th-Order Superintegrable Classical Systems Separating in Cartesian Coordinates Article published earlier |
| spellingShingle | Doubly Exotic th-Order Superintegrable Classical Systems Separating in Cartesian Coordinates Yurduşen, İsmet Escobar-Ruiz, Adrián Mauricio Palma y Meza Montoya, Irlanda |
| title | Doubly Exotic th-Order Superintegrable Classical Systems Separating in Cartesian Coordinates |
| title_full | Doubly Exotic th-Order Superintegrable Classical Systems Separating in Cartesian Coordinates |
| title_fullStr | Doubly Exotic th-Order Superintegrable Classical Systems Separating in Cartesian Coordinates |
| title_full_unstemmed | Doubly Exotic th-Order Superintegrable Classical Systems Separating in Cartesian Coordinates |
| title_short | Doubly Exotic th-Order Superintegrable Classical Systems Separating in Cartesian Coordinates |
| title_sort | doubly exotic th-order superintegrable classical systems separating in cartesian coordinates |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211629 |
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