Manifold Ways to Darboux-Halphen System
Many distinct problems give birth to the Darboux-Halphen system of differential equations, and here we review some of them. The first is the classical problem presented by Darboux and later solved by Halphen concerning finding an infinite number of double orthogonal surfaces in R³. The second is a p...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
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| Sprache: | English |
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Інститут математики НАН України
2018
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| Zitieren: | Manifold Ways to Darboux-Halphen System / J.A.C. Morales, H. Movasati, Y. Nikdelan, R. Roychowdhury, M.A.C. Torres // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 30 назв. — англ. |
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Morales, J.A.C. Movasati, H. Nikdelan, Y. Roychowdhury, R. Torres, M.A.C. 2025-11-21T19:15:28Z 2018 Manifold Ways to Darboux-Halphen System / J.A.C. Morales, H. Movasati, Y. Nikdelan, R. Roychowdhury, M.A.C. Torres // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 30 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 34M55; 53D45; 83C05 arXiv: 1709.09682 https://nasplib.isofts.kiev.ua/handle/123456789/209461 https://doi.org/10.3842/SIGMA.2018.003 Many distinct problems give birth to the Darboux-Halphen system of differential equations, and here we review some of them. The first is the classical problem presented by Darboux and later solved by Halphen concerning finding an infinite number of double orthogonal surfaces in R³. The second is a problem in general relativity about a gravitational instanton in the Bianchi IX metric space. The third problem stems from the new take on the moduli of enhanced elliptic curves called the Gauss-Manin connection in disguise, developed by one of the authors, and finally, in the last problem Darboux-Halphen system emerges from the associative algebra on the tangent space of a Frobenius manifold. During the manuscript preparation period, MACT was fully sponsored by CNpQ-Brasil. The research of RR was supported by FAPESP through the Instituto de Física, Universidade de São Paulo, with grant number 2013/17765-0. The work was initiated during the visit of RR to IMPA. He would like to thank IMPA for the hospitality during the course of this project. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Manifold Ways to Darboux-Halphen System Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Manifold Ways to Darboux-Halphen System |
| spellingShingle |
Manifold Ways to Darboux-Halphen System Morales, J.A.C. Movasati, H. Nikdelan, Y. Roychowdhury, R. Torres, M.A.C. |
| title_short |
Manifold Ways to Darboux-Halphen System |
| title_full |
Manifold Ways to Darboux-Halphen System |
| title_fullStr |
Manifold Ways to Darboux-Halphen System |
| title_full_unstemmed |
Manifold Ways to Darboux-Halphen System |
| title_sort |
manifold ways to darboux-halphen system |
| author |
Morales, J.A.C. Movasati, H. Nikdelan, Y. Roychowdhury, R. Torres, M.A.C. |
| author_facet |
Morales, J.A.C. Movasati, H. Nikdelan, Y. Roychowdhury, R. Torres, M.A.C. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
Many distinct problems give birth to the Darboux-Halphen system of differential equations, and here we review some of them. The first is the classical problem presented by Darboux and later solved by Halphen concerning finding an infinite number of double orthogonal surfaces in R³. The second is a problem in general relativity about a gravitational instanton in the Bianchi IX metric space. The third problem stems from the new take on the moduli of enhanced elliptic curves called the Gauss-Manin connection in disguise, developed by one of the authors, and finally, in the last problem Darboux-Halphen system emerges from the associative algebra on the tangent space of a Frobenius manifold.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209461 |
| citation_txt |
Manifold Ways to Darboux-Halphen System / J.A.C. Morales, H. Movasati, Y. Nikdelan, R. Roychowdhury, M.A.C. Torres // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 30 назв. — англ. |
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| first_indexed |
2025-12-07T18:35:40Z |
| last_indexed |
2025-12-07T18:35:40Z |
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1850886074567491584 |