On Uniqueness of Submaximally Symmetric Vector Ordinary Differential Equations of C-Class
The fundamental invariants for vector ODEs of order ≥ 3 considered up to point transformations consist of generalized Wilczynski invariants and C-class invariants. An ODE of C-class is characterized by the vanishing of the former. For any fixed C-class invariant , we give a local (point) classificat...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2023 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2023
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211971 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On Uniqueness of Submaximally Symmetric Vector Ordinary Differential Equations of C-Class. Johnson Allen Kessy and Dennis The. SIGMA 19 (2023), 058, 29 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862529412393598976 |
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| author | Kessy, Johnson Allen The, Dennis |
| author_facet | Kessy, Johnson Allen The, Dennis |
| citation_txt | On Uniqueness of Submaximally Symmetric Vector Ordinary Differential Equations of C-Class. Johnson Allen Kessy and Dennis The. SIGMA 19 (2023), 058, 29 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The fundamental invariants for vector ODEs of order ≥ 3 considered up to point transformations consist of generalized Wilczynski invariants and C-class invariants. An ODE of C-class is characterized by the vanishing of the former. For any fixed C-class invariant , we give a local (point) classification for all submaximally symmetric ODEs of C-class with ≢ 0 and all remaining C-class invariants vanishing identically. Our results yield generalizations of a well-known classical result for scalar ODEs due to Sophus Lie. Fundamental invariants correspond to the harmonic curvature of the associated Cartan geometry. A key new ingredient underlying our classification results is an advance concerning the harmonic theory associated with the structure of vector ODEs of C-class. Namely, for each irreducible C-class module, we provide an explicit identification of a lowest weight vector as a harmonic 2-cochain.
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| first_indexed | 2026-03-12T12:31:13Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211971 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-12T12:31:13Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kessy, Johnson Allen The, Dennis 2026-01-20T16:11:53Z 2023 On Uniqueness of Submaximally Symmetric Vector Ordinary Differential Equations of C-Class. Johnson Allen Kessy and Dennis The. SIGMA 19 (2023), 058, 29 pages 1815-0659 2020 Mathematics Subject Classification: 35B06; 53A55; 17B66; 57M60 arXiv:2301.09364 https://nasplib.isofts.kiev.ua/handle/123456789/211971 https://doi.org/10.3842/SIGMA.2023.058 The fundamental invariants for vector ODEs of order ≥ 3 considered up to point transformations consist of generalized Wilczynski invariants and C-class invariants. An ODE of C-class is characterized by the vanishing of the former. For any fixed C-class invariant , we give a local (point) classification for all submaximally symmetric ODEs of C-class with ≢ 0 and all remaining C-class invariants vanishing identically. Our results yield generalizations of a well-known classical result for scalar ODEs due to Sophus Lie. Fundamental invariants correspond to the harmonic curvature of the associated Cartan geometry. A key new ingredient underlying our classification results is an advance concerning the harmonic theory associated with the structure of vector ODEs of C-class. Namely, for each irreducible C-class module, we provide an explicit identification of a lowest weight vector as a harmonic 2-cochain. The authors acknowledge the use of the DifferentialGeometry package in Maple. We also acknowledge helpful conversations with Boris Kruglikov, Andreu Llabres, and Eivind Schneider. The research leading to these results has received funding from the Norwegian Financial Mechanism 2014–2021 (project registration number 2019/34/H/ST1/00636), the Tromsø Research Foundation (project “Pure Mathematics in Norway”), and the UiT Aurora project MASCOT, and this article/publication is based upon work from COST Action CaLISTA CA21109 supported by COST (European Cooperation in Science and Technology), https://www.cost.eu. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Uniqueness of Submaximally Symmetric Vector Ordinary Differential Equations of C-Class Article published earlier |
| spellingShingle | On Uniqueness of Submaximally Symmetric Vector Ordinary Differential Equations of C-Class Kessy, Johnson Allen The, Dennis |
| title | On Uniqueness of Submaximally Symmetric Vector Ordinary Differential Equations of C-Class |
| title_full | On Uniqueness of Submaximally Symmetric Vector Ordinary Differential Equations of C-Class |
| title_fullStr | On Uniqueness of Submaximally Symmetric Vector Ordinary Differential Equations of C-Class |
| title_full_unstemmed | On Uniqueness of Submaximally Symmetric Vector Ordinary Differential Equations of C-Class |
| title_short | On Uniqueness of Submaximally Symmetric Vector Ordinary Differential Equations of C-Class |
| title_sort | on uniqueness of submaximally symmetric vector ordinary differential equations of c-class |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211971 |
| work_keys_str_mv | AT kessyjohnsonallen onuniquenessofsubmaximallysymmetricvectorordinarydifferentialequationsofcclass AT thedennis onuniquenessofsubmaximallysymmetricvectorordinarydifferentialequationsofcclass |